Time, Speed, and Distance

Mathematics

Class 5 | CBSE, NCERT & ICSE

Learning Objectives

Understand the relationship between speed, distance, and time
Use the formula: Speed = Distance ÷ Time
Use the formula: Distance = Speed × Time
Use the formula: Time = Distance ÷ Speed
Convert between hours and minutes for calculations
Convert between km/h and m/s
Understand and calculate average speed
Solve word problems involving travel in Indian contexts

Introduction — Speed in Our Daily Life

Every day, we travel from one place to another — walking to school, cycling to the park, riding in a car, or taking a train. Have you ever wondered: How fast am I going? How long will this trip take? How far have I travelled?

When your family takes the Rajdhani Express from Delhi to Mumbai, the train covers about 1,384 km in 16 hours. The Vande Bharat Express from Delhi to Varanasi covers 759 km in just 8 hours! A car on the National Highway might travel at 80 km/h, while you walk to school at about 4 km/h.

In this chapter, we will learn the mathematical relationship between Speed, Distance, and Time — and how to calculate one when we know the other two. This is one of the most useful maths concepts in real life!

What is Speed?

Speed tells us how fast something is moving. It measures the distance covered in a given unit of time.

Definition

Speed = The distance covered per unit time
If a car covers 60 km in 1 hour, its speed is 60 km per hour (written as 60 km/h)
If a person walks 100 metres in 1 minute, their speed is 100 m per minute (100 m/min)

Units of Speed

Unit	Written As	Used For
Kilometres per hour	km/h or km/hr	Cars, trains, buses, planes
Metres per second	m/s	Running, cycling, science experiments
Metres per minute	m/min	Walking, jogging

Comparing Speeds

Object / Person	Approximate Speed
Person walking	4–5 km/h
Person cycling	12–18 km/h
Auto-rickshaw in city	25–35 km/h
Car on highway	60–100 km/h
Vande Bharat Express	130–160 km/h
Rajdhani Express	80–130 km/h
Aeroplane	800–900 km/h
Speed of sound	1,235 km/h

Image needed: A speedometer-style visual comparing different speeds — walking person (5 km/h), cyclist (15 km/h), car (60 km/h), train (120 km/h), aeroplane (850 km/h). Each with a small icon and speed label arranged from slow to fast.
Style: Colourful flat illustration, horizontal layout with speed indicators, child-friendly icons
Size: 800×350px

Think About It: A cheetah can run at 120 km/h — as fast as a train! But it can only maintain that speed for about 30 seconds. Humans can run at about 10–12 km/h. Usain Bolt's top speed was nearly 45 km/h!

The Speed-Distance-Time Triangle

Speed, Distance, and Time are connected by a simple relationship. If you know any two of these, you can always find the third one using these formulas:

The Three Formulas

Speed = Distance ÷ Time (S = D ÷ T)
Distance = Speed × Time (D = S × T)
Time = Distance ÷ Speed (T = D ÷ S)

Image needed: The Speed-Distance-Time triangle diagram. A triangle with D (Distance) at the top, S (Speed) at the bottom-left, and T (Time) at the bottom-right. A horizontal line separates D from S and T. A vertical line separates S and T. Show the three formulas derived from covering one letter: cover D to get S×T, cover S to get D÷T, cover T to get D÷S.
Style: Clean diagram with bright colours, large clear letters, arrows showing each formula derivation
Size: 600×500px

How to Use the Triangle

The triangle is an easy memory trick:

To find Distance: Cover D — you see S × T (Speed times Time)
To find Speed: Cover S — you see D ÷ T (Distance divided by Time)
To find Time: Cover T — you see D ÷ S (Distance divided by Speed)

Remember it this way: Distance is always on TOP of the triangle. Speed and Time are at the BOTTOM. When the two bottom values are side by side, you multiply. When one is on top and one is on the bottom, you divide.

Finding Speed (When Distance and Time Are Given)

Formula

Speed = Distance ÷ Time

Example 1: A train travels 450 km in 5 hours. Find its speed.

Speed = Distance ÷ Time
Speed = 450 ÷ 5 = 90 km/h

The train's speed is 90 km/h.

Example 2: Arjun cycles 24 km in 2 hours to reach his grandparents' house. What is his cycling speed?

Speed = Distance ÷ Time
Speed = 24 ÷ 2 = 12 km/h

Arjun cycles at 12 km/h.

Example 3: The Vande Bharat Express covers 759 km from Delhi to Varanasi in 8 hours. Find its speed.

Speed = Distance ÷ Time
Speed = 759 ÷ 8 = 94.875 km/h
(approximately 95 km/h)

Example 4: Meena walks 3,000 metres in 40 minutes. What is her speed in m/min?

Speed = Distance ÷ Time
Speed = 3,000 ÷ 40 = 75 m/min

Meena walks at 75 metres per minute.

Example 5: An aeroplane flies from Delhi to Bengaluru (1,740 km) in 2 hours 30 minutes. Find its speed.

First, convert time: 2 hours 30 minutes = 2.5 hours
Speed = Distance ÷ Time
Speed = 1,740 ÷ 2.5 = 696 km/h

Finding Distance (When Speed and Time Are Given)

Formula

Distance = Speed × Time

Example 1: A car travels at 80 km/h for 3 hours. How far does it go?

Distance = Speed × Time
Distance = 80 × 3 = 240 km

Example 2: Dhruv rides his bicycle at 15 km/h for 2 hours. What distance does he cover?

Distance = Speed × Time
Distance = 15 × 2 = 30 km

Example 3: The Rajdhani Express travels at 110 km/h. How far will it go in 6 hours?

Distance = Speed × Time
Distance = 110 × 6 = 660 km

Example 4: A runner runs at 200 m/min. How far will she run in 15 minutes?

Distance = Speed × Time
Distance = 200 × 15 = 3,000 m = 3 km

Example 5: An auto-rickshaw in Jaipur moves at 30 km/h. How far will it travel in 1 hour 30 minutes?

Time = 1 hour 30 min = 1.5 hours
Distance = Speed × Time
Distance = 30 × 1.5 = 45 km

Finding Time (When Speed and Distance Are Given)

Formula

Time = Distance ÷ Speed

Example 1: A bus travels 240 km at a speed of 60 km/h. How long does the journey take?

Time = Distance ÷ Speed
Time = 240 ÷ 60 = 4 hours

Example 2: Akriti walks 6 km to school at 4 km/h. How long does it take her?

Time = Distance ÷ Speed
Time = 6 ÷ 4 = 1.5 hours = 1 hour 30 minutes

Example 3: A train covers 840 km at 120 km/h. How long is the journey?

Time = Distance ÷ Speed
Time = 840 ÷ 120 = 7 hours

Example 4: Ravi's father drives at 75 km/h on the Delhi-Jaipur highway. The distance is 280 km. How long will the drive take?

Time = Distance ÷ Speed
Time = 280 ÷ 75 = 3.73 hours
= 3 hours + (0.73 × 60) minutes
= 3 hours 44 minutes (approximately)

Example 5: A cyclist rides at 18 km/h. How long will it take to cover 45 km?

Time = Distance ÷ Speed
Time = 45 ÷ 18 = 2.5 hours = 2 hours 30 minutes

Converting Time Units

In speed-distance-time problems, time must be in the correct unit. If speed is in km/h, time must be in hours. If speed is in m/min, time must be in minutes.

Time Conversion Rules

1 hour = 60 minutes
1 minute = 60 seconds
Hours to minutes: Multiply by 60
Minutes to hours: Divide by 60

Image needed: A visual showing time conversion — a clock face with arrows showing hours to minutes (×60) and minutes to hours (÷60). Also show minutes to seconds (×60) and seconds to minutes (÷60). Use bright arrows and clear labels.
Style: Clean infographic with clock icon, conversion arrows in different colours
Size: 600×400px

Converting Hours and Minutes to Hours (Decimal)

When time is given as "hours and minutes," convert to decimal hours for easy calculation.

Examples:

Time (hrs & min)	As Minutes	As Decimal Hours	Method
1 hour 30 min	90 min	1.5 hours	30 ÷ 60 = 0.5
2 hours 15 min	135 min	2.25 hours	15 ÷ 60 = 0.25
3 hours 45 min	225 min	3.75 hours	45 ÷ 60 = 0.75
4 hours 20 min	260 min	4.33 hours	20 ÷ 60 = 0.33
2 hours 40 min	160 min	2.67 hours	40 ÷ 60 = 0.67

Converting Decimal Hours Back to Hours and Minutes

Example: Convert 3.25 hours to hours and minutes.

Whole part = 3 hours
Decimal part = 0.25 hours = 0.25 × 60 = 15 minutes
Answer: 3 hours 15 minutes

Example: Convert 2.75 hours to hours and minutes.

Whole part = 2 hours
Decimal part = 0.75 hours = 0.75 × 60 = 45 minutes
Answer: 2 hours 45 minutes

Quick Tip: Some common decimal-to-minute conversions to remember: 0.25 hours = 15 min, 0.5 hours = 30 min, 0.75 hours = 45 min. These come up very often in problems!

Converting Speed Units

Sometimes we need to convert speed from one unit to another. The two most common conversions are between km/h and m/s.

Conversion Formulas

km/h to m/s: Multiply by 5/18 (or divide by 3.6)
m/s to km/h: Multiply by 18/5 (or multiply by 3.6)

Why 5/18?

Understanding the conversion:
1 km = 1,000 metres
1 hour = 3,600 seconds (60 × 60)

So, 1 km/h = 1,000 m ÷ 3,600 s = 1000/3600 = 5/18 m/s

And 1 m/s = 3,600/1,000 km/h = 18/5 km/h = 3.6 km/h

Converting km/h to m/s

Example 1: Convert 90 km/h to m/s.
90 × 5/18 = 450/18 = 25 m/s

Example 2: Convert 72 km/h to m/s.
72 × 5/18 = 360/18 = 20 m/s

Example 3: Convert 36 km/h to m/s.
36 × 5/18 = 180/18 = 10 m/s

Converting m/s to km/h

Example 4: Convert 15 m/s to km/h.
15 × 18/5 = 270/5 = 54 km/h

Example 5: Convert 30 m/s to km/h.
30 × 18/5 = 540/5 = 108 km/h

Easy Trick: When converting km/h to m/s, the answer always gets smaller (because seconds are much smaller than hours). When converting m/s to km/h, the answer always gets larger. Use this to check if your answer makes sense!

Average Speed

When a vehicle does not travel at the same speed throughout its journey (it speeds up, slows down, stops at signals), we use average speed to describe how fast it went overall.

Formula

Average Speed = Total Distance ÷ Total Time

Image needed: A visual showing a car journey in two parts — Part 1 at 60 km/h for 2 hours, Part 2 at 40 km/h for 3 hours. Show a road with two segments, speed labels on each, and total distance/time calculation at the bottom. Indian road setting with highway markers.
Style: Simple infographic with road illustration, speed labels, calculation shown
Size: 750×350px

Example 1: A car travels 120 km in the first 2 hours and then 80 km in the next 2 hours. Find its average speed.

Total Distance = 120 + 80 = 200 km
Total Time = 2 + 2 = 4 hours
Average Speed = 200 ÷ 4 = 50 km/h

Example 2: Sita's school bus travels at 40 km/h for the first 30 minutes, then at 20 km/h for the next 30 minutes (due to traffic). Find the average speed.

Distance in first part = 40 × 0.5 = 20 km
Distance in second part = 20 × 0.5 = 10 km
Total Distance = 20 + 10 = 30 km
Total Time = 0.5 + 0.5 = 1 hour
Average Speed = 30 ÷ 1 = 30 km/h

Example 3: A train travels from Delhi to Agra (200 km) at 100 km/h, and then from Agra to Jaipur (240 km) at 80 km/h. Find the average speed for the entire journey.

Time for Delhi to Agra = 200 ÷ 100 = 2 hours
Time for Agra to Jaipur = 240 ÷ 80 = 3 hours
Total Distance = 200 + 240 = 440 km
Total Time = 2 + 3 = 5 hours
Average Speed = 440 ÷ 5 = 88 km/h

Important: Average speed is NOT the same as the average of two speeds! In Example 3, the average of 100 and 80 is 90, but the actual average speed is 88 km/h. Always use the formula: Total Distance ÷ Total Time.

Word Problems — Indian Context

Let us solve some real-life problems involving travel in India:

Problem 1: The Rajdhani Express travels from New Delhi to Mumbai (1,384 km) in 16 hours. What is its average speed?

Solution:
Speed = Distance ÷ Time
Speed = 1,384 ÷ 16 = 86.5 km/h

Problem 2: Hridan cycles to school at 12 km/h. His school is 3 km from his house. How many minutes does it take him?

Solution:
Time = Distance ÷ Speed
Time = 3 ÷ 12 = 0.25 hours
0.25 × 60 = 15 minutes

Problem 3: A family drives from Bengaluru to Mysuru at 80 km/h. The distance is 150 km. They start at 8:00 AM. At what time will they reach?

Solution:
Time = Distance ÷ Speed = 150 ÷ 80 = 1.875 hours
1.875 hours = 1 hour + (0.875 × 60) min = 1 hour 52.5 minutes
Start time: 8:00 AM + 1 hr 53 min ≈ 9:53 AM

Problem 4: An IndiGo flight from Delhi to Chennai takes 2 hours 30 minutes. If the plane flies at 680 km/h, what is the distance between Delhi and Chennai?

Solution:
Time = 2.5 hours
Distance = Speed × Time = 680 × 2.5 = 1,700 km

Problem 5: Bianca's father drives from Pune to Mumbai (150 km). He drives at 60 km/h for the first half of the distance and 50 km/h for the second half. Find his average speed.

Solution:
First half: Distance = 75 km, Speed = 60 km/h, Time = 75 ÷ 60 = 1.25 hours
Second half: Distance = 75 km, Speed = 50 km/h, Time = 75 ÷ 50 = 1.5 hours
Total Distance = 150 km
Total Time = 1.25 + 1.5 = 2.75 hours
Average Speed = 150 ÷ 2.75 = 54.5 km/h (approximately)

Image needed: A simplified railway map of India showing distances between major cities — Delhi, Mumbai (1384 km), Chennai (2175 km from Delhi), Kolkata (1305 km from Delhi), Bengaluru (2150 km from Delhi), Jaipur (280 km from Delhi). Train icons on routes with distance labels.
Style: Colourful simplified map with city dots, distance labels, train icons, child-friendly
Size: 700×600px

Key Words

Term	Meaning
Speed	The distance covered per unit time (how fast something moves)
Distance	The total length of the path travelled (measured in km or m)
Time	How long the journey takes (measured in hours, minutes, or seconds)
km/h	Kilometres per hour — speed unit for vehicles
m/s	Metres per second — speed unit used in science
Average Speed	Total distance divided by total time for the whole journey
Uniform Speed	Same speed throughout the journey (constant speed)
Variable Speed	Speed that changes during the journey
Convert	Change from one unit to another (e.g., hours to minutes)

Key Points to Remember

Speed = Distance ÷ Time (when you know how far and how long)
Distance = Speed × Time (when you know how fast and how long)
Time = Distance ÷ Speed (when you know how far and how fast)
Always check that units match — if speed is km/h, time must be in hours and distance in km.
1 hour = 60 minutes. To convert minutes to hours, divide by 60.
km/h to m/s: Multiply by 5/18. m/s to km/h: Multiply by 18/5.
Average Speed = Total Distance ÷ Total Time (NOT the average of two speeds!).
The Speed-Distance-Time triangle: D on top, S and T at bottom. Cover what you need to find.
If an answer comes in decimal hours, convert: multiply the decimal part by 60 to get minutes.

Finished learning? Now test what you know!

🎯 Quick Quiz — Test Yourself!

Answer these questions right here. You get instant feedback — no paper needed!

Score: 0 / 8

1. Which formula finds distance?

Distance = Speed × Time.

2. A car travels 60 km in 1 hour. Its speed is:

Speed = Distance ÷ Time = 60 ÷ 1 = 60 km/h.

3. How many minutes are there in 2 hours?

1 hour = 60 minutes, so 2 hours = 120 minutes.

4. A train covers 240 km in 4 hours. Its speed is:

Speed = 240 ÷ 4 = 60 km/h.

5. A bus travels at 50 km/h for 3 hours. How far does it go? (km, digits only)

Distance = Speed × Time = 50 × 3 = 150 km.

6. A cyclist covers 45 km at 15 km/h. How many hours does it take?

Time = Distance ÷ Speed = 45 ÷ 15 = 3 hours.

7. How many minutes are there in one and a half hours? (digits only)

1½ hours = 60 + 30 = 90 minutes.

8. A car goes 210 km in 3 hours. Find its speed in km/h (digits only):

Speed = 210 ÷ 3 = 70 km/h.

Practice Questions

A. Find the Speed:

1. A bus covers 350 km in 5 hours. Find its speed.

2. Arjun runs 800 metres in 4 minutes. What is his speed in m/min?

3. A train travels 540 km in 6 hours. Find its speed in km/h.

4. An aeroplane flies 4,200 km in 5 hours. What is its speed?

5. Meena walks 2.4 km in 30 minutes. Find her speed in km/h.

6. A ship sails 180 km in 9 hours. What is its speed?

B. Find the Distance:

1. A car travels at 75 km/h for 4 hours. How far does it go?

2. A cyclist rides at 16 km/h for 2 hours 30 minutes. Find the distance.

3. A train moves at 95 km/h for 8 hours. What distance does it cover?

4. Ravi jogs at 150 m/min for 20 minutes. How far does he jog?

5. An express train travels at 120 km/h for 3 hours 15 minutes. Find the distance.

6. A boat moves at 25 km/h for 6 hours. How far does it travel?

C. Find the Time:

1. A bus covers 360 km at 60 km/h. How long does the journey take?

2. A car travels 150 km at 50 km/h. Find the time taken.

3. An athlete runs 5,000 m at 250 m/min. How many minutes does it take?

4. A train covers 1,050 km at 150 km/h. Find the time.

5. Dhruv cycles 21 km at 14 km/h. How long does it take?

6. A plane flies 3,600 km at 900 km/h. Find the time in hours.

D. Convert Time Units:

1. Convert 3 hours 45 minutes to hours (decimal):

2. Convert 2 hours 20 minutes to minutes:

3. Convert 150 minutes to hours and minutes:

4. Convert 4.5 hours to hours and minutes:

5. Convert 2.75 hours to hours and minutes:

E. Convert Speed Units:

1. Convert 54 km/h to m/s:

2. Convert 108 km/h to m/s:

3. Convert 20 m/s to km/h:

4. Convert 25 m/s to km/h:

F. Average Speed:

1. A car travels 100 km in 2 hours and then 60 km in 1 hour. Find the average speed.

2. A bus goes from Delhi to Agra (200 km) at 50 km/h and returns at 40 km/h. Find the average speed for the round trip.

3. Akriti walks 2 km at 4 km/h and then runs 3 km at 6 km/h. What is her average speed?

G. Fill in the Blanks:

1. Speed = ÷

2. Distance = ×

3. If a car travels at 60 km/h for 3 hours, it covers km.

4. 1 km/h = m/s (fraction).

5. Average Speed = ÷

H. Choose the Correct Answer (MCQ):

1. A car covers 240 km in 4 hours. Its speed is:

a) 40 km/h b) 60 km/h c) 80 km/h d) 50 km/h

2. A train travels at 90 km/h for 5 hours. The distance covered is:

a) 450 km b) 400 km c) 500 km d) 360 km

3. 72 km/h is equal to:

a) 10 m/s b) 20 m/s c) 36 m/s d) 72 m/s

4. A cyclist covers 30 km at 15 km/h. The time taken is:

a) 1 hour b) 2 hours c) 3 hours d) 1.5 hours

I. Word Problems:

1. The Shatabdi Express travels from Delhi to Chandigarh (250 km) at 100 km/h. At what time will it reach if it starts at 7:00 AM?

2. Ravi's family drives from Mumbai to Goa (590 km). They drive at 80 km/h for the first 3 hours and 60 km/h for the remaining distance. Find: (a) the remaining distance, and (b) the total time for the journey.

3. Meena walks to school (1.5 km) at 5 km/h. Her brother Arjun cycles the same distance at 15 km/h. How many minutes earlier does Arjun reach?

4. A goods train travels at 45 km/h. An express train travels the same 360 km route at 90 km/h. How much time does the express train save?

5. Two cities are 600 km apart. Train A leaves City 1 at 60 km/h. Train B leaves City 2 at the same time at 40 km/h, travelling towards City 1. After how many hours will they meet?

6. A delivery truck on NH-48 covers 420 km from Delhi to Jaipur via Gurugram. It travels at 70 km/h for the first 210 km and 60 km/h for the rest. Find the total time and average speed.

Activity — Travel Planner!

You are planning train journeys across India! Use the distances and speeds given below to calculate how long each journey will take. Fill in the table:

Route	Distance (km)	Train Speed (km/h)
Delhi to Jaipur	280	70
Mumbai to Pune	150	75
Chennai to Bengaluru	350	100
Kolkata to Patna	530	80
Delhi to Lucknow	500	125
Hyderabad to Vizag	620	80

Bonus Challenge: If a Vande Bharat Express could cover Delhi to Mumbai (1,384 km) at 160 km/h non-stop, how long would the journey take? Compare this with the Rajdhani's time of 16 hours!

Want to review the lesson again?

Mathematics

Time, Speed, and Distance

Class 5 | CBSE / NCERT / ICSE

Name: Class: Date:

Learning Objectives

Understand the relationship between speed, distance, and time
Use formulas to find speed, distance, or time
Convert between hours and minutes
Convert between km/h and m/s
Calculate average speed
Solve word problems involving travel

Introduction — Speed in Our Daily Life

Every day we travel — walking, cycling, riding in cars or trains. The Rajdhani Express covers 1,384 km in 16 hours. A car on the highway travels at 80 km/h. We walk at about 4 km/h. In this chapter, we learn how Speed, Distance, and Time are related, and how to calculate one when we know the other two.

What is Speed?

Speed = Distance covered per unit time. It tells us how fast something is moving.

Unit	Written As	Used For
Kilometres per hour	km/h	Cars, trains, planes
Metres per second	m/s	Running, science
Metres per minute	m/min	Walking, jogging

Object	Speed
Walking	4–5 km/h
Cycling	12–18 km/h
Car (highway)	60–100 km/h
Vande Bharat Express	130–160 km/h
Aeroplane	800–900 km/h

[Image: Speedometer visual — walking 5 km/h, cycling 15 km/h, car 60 km/h, train 120 km/h, plane 850 km/h]

The Speed-Distance-Time Triangle

The Three Formulas:
• Speed = Distance ÷ Time (S = D ÷ T)
• Distance = Speed × Time (D = S × T)
• Time = Distance ÷ Speed (T = D ÷ S)

[Image: Speed-Distance-Time triangle — D on top, S and T at bottom. Cover one to find the formula for it.]

How to use: Cover what you want to find. D on top, S and T at bottom. Side by side = multiply. Top over bottom = divide.

Finding Speed

Formula: Speed = Distance ÷ Time

Ex 1: Train travels 450 km in 5 hours. Speed = 450 ÷ 5 = 90 km/h
Ex 2: Arjun cycles 24 km in 2 hours. Speed = 24 ÷ 2 = 12 km/h
Ex 3: Vande Bharat: 759 km in 8 hours. Speed = 759 ÷ 8 = 95 km/h (approx)
Ex 4: Meena walks 3,000 m in 40 min. Speed = 3,000 ÷ 40 = 75 m/min
Ex 5: Plane: 1,740 km in 2.5 hrs. Speed = 1,740 ÷ 2.5 = 696 km/h

Finding Distance

Formula: Distance = Speed × Time

Ex 1: Car at 80 km/h for 3 hours. Distance = 80 × 3 = 240 km
Ex 2: Dhruv cycles at 15 km/h for 2 hours. Distance = 15 × 2 = 30 km
Ex 3: Rajdhani at 110 km/h for 6 hours. Distance = 110 × 6 = 660 km
Ex 4: Runner at 200 m/min for 15 min. Distance = 200 × 15 = 3,000 m = 3 km
Ex 5: Auto at 30 km/h for 1.5 hrs. Distance = 30 × 1.5 = 45 km

Finding Time

Formula: Time = Distance ÷ Speed

Ex 1: Bus: 240 km at 60 km/h. Time = 240 ÷ 60 = 4 hours
Ex 2: Akriti walks 6 km at 4 km/h. Time = 6 ÷ 4 = 1.5 hrs = 1 hr 30 min
Ex 3: Train: 840 km at 120 km/h. Time = 840 ÷ 120 = 7 hours
Ex 4: Car: 280 km at 75 km/h. Time = 280 ÷ 75 = 3.73 hrs ≈ 3 hrs 44 min
Ex 5: Cyclist: 45 km at 18 km/h. Time = 45 ÷ 18 = 2.5 hrs = 2 hrs 30 min

Converting Time Units

1 hour = 60 minutes | 1 minute = 60 seconds

Hours to minutes: × 60 | Minutes to hours: ÷ 60

[Image: Time conversion visual — clock with arrows showing hours ↔ minutes (×60 / ÷60)]

Time (hrs & min)	Decimal Hours	Method
1 hr 30 min	1.5 hours	30 ÷ 60 = 0.5
2 hrs 15 min	2.25 hours	15 ÷ 60 = 0.25
3 hrs 45 min	3.75 hours	45 ÷ 60 = 0.75
4 hrs 20 min	4.33 hours	20 ÷ 60 = 0.33

Decimal to hrs & min: 3.25 hrs = 3 hrs + (0.25 × 60) = 3 hrs 15 min
2.75 hrs = 2 hrs + (0.75 × 60) = 2 hrs 45 min

Quick tip: 0.25 hr = 15 min, 0.5 hr = 30 min, 0.75 hr = 45 min

Converting Speed Units

km/h to m/s: Multiply by 5/18
m/s to km/h: Multiply by 18/5

Why? 1 km/h = 1000 m ÷ 3600 s = 5/18 m/s

km/h → m/s:
90 km/h = 90 × 5/18 = 25 m/s
72 km/h = 72 × 5/18 = 20 m/s
36 km/h = 36 × 5/18 = 10 m/s

m/s → km/h:
15 m/s = 15 × 18/5 = 54 km/h
30 m/s = 30 × 18/5 = 108 km/h

Check: km/h to m/s → answer gets smaller. m/s to km/h → answer gets larger.

Average Speed

Average Speed = Total Distance ÷ Total Time
(NOT the average of two speeds!)

[Image: Average speed concept — car journey in two parts at different speeds, showing total distance and total time calculation]

Ex 1: Car: 120 km in 2 hrs + 80 km in 2 hrs. Avg Speed = 200 ÷ 4 = 50 km/h
Ex 2: Bus: 40 km/h for 30 min + 20 km/h for 30 min. D1=20km, D2=10km. Avg = 30 ÷ 1 = 30 km/h
Ex 3: Train: Delhi-Agra (200 km) at 100 km/h + Agra-Jaipur (240 km) at 80 km/h.
T1=2hrs, T2=3hrs. Total=440km, Time=5hrs. Avg = 440 ÷ 5 = 88 km/h

Word Problems — Indian Context

P1: Rajdhani: 1,384 km in 16 hrs. Speed = 1384 ÷ 16 = 86.5 km/h
P2: Hridan cycles 3 km at 12 km/h. Time = 3 ÷ 12 = 0.25 hrs = 15 min
P3: Family drives 150 km at 80 km/h, start 8AM. Time = 150÷80 = 1.875 hrs ≈ 1hr 53min. Reach: 9:53 AM
P4: Flight at 680 km/h for 2.5 hrs. Distance = 680 × 2.5 = 1,700 km
P5: Pune-Mumbai (150 km): 75 km at 60 km/h (1.25 hrs) + 75 km at 50 km/h (1.5 hrs). Avg = 150 ÷ 2.75 = 54.5 km/h

[Image: Indian railway map — Delhi, Mumbai, Chennai, Kolkata, Bengaluru, Jaipur with distances]

Key Words

Term	Meaning
Speed	Distance covered per unit time
Distance	Total path length travelled (km or m)
Time	Duration of journey (hours, minutes, seconds)
km/h	Kilometres per hour
m/s	Metres per second
Average Speed	Total distance ÷ Total time
Uniform Speed	Constant speed throughout
Variable Speed	Speed that changes during journey

Key Points:
• Speed = Distance ÷ Time | Distance = Speed × Time | Time = Distance ÷ Speed
• Units must match: km/h with hours/km, m/s with seconds/metres
• 1 hour = 60 min. Minutes to hours: ÷ 60. Hours to minutes: × 60
• km/h to m/s: × 5/18. m/s to km/h: × 18/5
• Average Speed = Total Distance ÷ Total Time (not average of speeds)
• D-S-T triangle: D on top, S and T below. Cover what you need.
• Decimal hours to minutes: multiply decimal part by 60

Practice Questions

A. Find the Speed:

1. A bus covers 350 km in 5 hours. Speed =

2. Arjun runs 800 m in 4 minutes. Speed = m/min

3. A train travels 540 km in 6 hours. Speed =

4. A plane flies 4,200 km in 5 hours. Speed =

5. Meena walks 2.4 km in 30 min. Speed = km/h

6. A ship sails 180 km in 9 hours. Speed =

B. Find the Distance:

1. Car at 75 km/h for 4 hours. Distance =

2. Cyclist at 16 km/h for 2 hrs 30 min. Distance =

3. Train at 95 km/h for 8 hours. Distance =

4. Ravi jogs at 150 m/min for 20 min. Distance =

5. Express train at 120 km/h for 3 hrs 15 min. Distance =

6. Boat at 25 km/h for 6 hours. Distance =

C. Find the Time:

1. Bus: 360 km at 60 km/h. Time =

2. Car: 150 km at 50 km/h. Time =

3. Athlete: 5,000 m at 250 m/min. Time =

4. Train: 1,050 km at 150 km/h. Time =

5. Dhruv cycles 21 km at 14 km/h. Time =

6. Plane: 3,600 km at 900 km/h. Time =

D. Convert Time Units:

1. 3 hrs 45 min = hours (decimal)

2. 2 hrs 20 min = minutes

3. 150 minutes = hrs min

4. 4.5 hours = hrs min

5. 2.75 hours = hrs min

E. Convert Speed Units:

1. 54 km/h = m/s

2. 108 km/h = m/s

3. 20 m/s = km/h

4. 25 m/s = km/h

F. Average Speed:

1. Car: 100 km in 2 hrs, then 60 km in 1 hr. Avg speed =

2. Bus: Delhi-Agra (200 km) at 50 km/h, returns at 40 km/h. Avg speed for round trip?

3. Akriti walks 2 km at 4 km/h, runs 3 km at 6 km/h. Avg speed?

G. Fill in the Blanks:

1. Speed = ÷

2. Distance = ×

3. Car at 60 km/h for 3 hours covers km.

4. 1 km/h = m/s (fraction).

5. Average Speed = ÷

H. Choose the Correct Answer (MCQ):

1. A car covers 240 km in 4 hours. Its speed is:

a) 40 km/h b) 60 km/h c) 80 km/h d) 50 km/h

2. Train at 90 km/h for 5 hours. Distance =

a) 450 km b) 400 km c) 500 km d) 360 km

3. 72 km/h is equal to:

a) 10 m/s b) 20 m/s c) 36 m/s d) 72 m/s

4. Cyclist covers 30 km at 15 km/h. Time =

a) 1 hour b) 2 hours c) 3 hours d) 1.5 hours

I. Word Problems:

1. Shatabdi Express: Delhi-Chandigarh (250 km) at 100 km/h, starts 7:00 AM. Arrival time?

2. Mumbai-Goa (590 km): 80 km/h for 3 hrs, then 60 km/h for rest. Find remaining distance and total time.

3. Meena walks 1.5 km at 5 km/h. Arjun cycles same at 15 km/h. How many minutes earlier does Arjun reach?

4. Goods train at 45 km/h and express at 90 km/h cover 360 km. Time saved by express?

5. Cities 600 km apart. Train A at 60 km/h and Train B at 40 km/h travel towards each other. When do they meet?

6. Truck: 420 km, first 210 km at 70 km/h, rest at 60 km/h. Total time and average speed?

Activity — Travel Planner!

Plan train journeys! Calculate how long each journey takes:

Route	Distance (km)	Speed (km/h)
Delhi to Jaipur	280	70
Mumbai to Pune	150	75
Chennai to Bengaluru	350	100
Kolkata to Patna	530	80
Delhi to Lucknow	500	125
Hyderabad to Vizag	620	80

Bonus: Vande Bharat at 160 km/h for Delhi-Mumbai (1,384 km). Time =

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