Speed, Time and Distance Word Problems
Speed, time, and distance are connected by a simple relationship. If you know any two of these three quantities, you can calculate the third. These problems describe real-life situations: a car driving between cities, a train journey, a cyclist riding to school, or an athlete running a race.
In Class 5, you will learn the formulas connecting speed, time, and distance, and apply them to solve word problems. The key skill is reading the problem, identifying what is given and what is asked, and choosing the correct formula.
Speed is measured in km/h (kilometres per hour) or m/s (metres per second). Time is in hours, minutes, or seconds. Distance is in km or m.
What is Speed, Time and Distance Word Problems - Class 5 Maths (Time)?
Speed is how fast an object moves. It tells the distance covered in one unit of time.
- Speed = Distance ÷ Time
- Distance = Speed × Time
- Time = Distance ÷ Speed
Units:
- If distance is in km and time in hours, speed is in km/h (kilometres per hour).
- If distance is in m and time in seconds, speed is in m/s (metres per second).
Speed, Time and Distance Word Problems Formula
Speed = Distance ÷ Time
Distance = Speed × Time
Time = Distance ÷ Speed
Types and Properties
Types of speed-time-distance problems:
- Finding speed: Given distance and time.
- Finding distance: Given speed and time.
- Finding time: Given speed and distance.
- Comparing speeds: Who is faster?
- Two-part journeys: Different speeds for different parts.
- Unit conversion: Converting km/h to m/s or vice versa.
Solved Examples
Example 1: Example 1: Finding Speed
Problem: A car covers 240 km in 4 hours. Find its speed.
Solution:
Step 1: Speed = Distance ÷ Time = 240 ÷ 4 = 60 km/h
Answer: The speed of the car is 60 km/h.
Example 2: Example 2: Finding Distance
Problem: A train travels at 80 km/h for 3 hours. How far does it go?
Solution:
Step 1: Distance = Speed × Time = 80 × 3 = 240 km
Answer: The train covers 240 km.
Example 3: Example 3: Finding Time
Problem: Priya cycles at 12 km/h. How long will she take to cover 36 km?
Solution:
Step 1: Time = Distance ÷ Speed = 36 ÷ 12 = 3 hours
Answer: Priya will take 3 hours.
Example 4: Example 4: Comparing Speeds
Problem: Arjun runs 100 m in 20 seconds. Dev runs 80 m in 16 seconds. Who is faster?
Solution:
Arjun’s speed = 100 ÷ 20 = 5 m/s
Dev’s speed = 80 ÷ 16 = 5 m/s
Answer: Both have the same speed (5 m/s).
Example 5: Example 5: Two-Part Journey
Problem: Aman drives 120 km at 60 km/h, then another 80 km at 40 km/h. Find the total time.
Solution:
Step 1: Time for part 1 = 120 ÷ 60 = 2 hours
Step 2: Time for part 2 = 80 ÷ 40 = 2 hours
Step 3: Total time = 2 + 2 = 4 hours
Answer: The total time is 4 hours.
Example 6: Example 6: Train Problem
Problem: The Rajdhani Express travels from Delhi to Mumbai (1,384 km) in approximately 16 hours. Estimate its average speed.
Solution:
Step 1: Speed = 1,384 ÷ 16 ≈ 86.5 km/h
Answer: The average speed is approximately 86.5 km/h.
Example 7: Example 7: Auto-Rickshaw Ride
Problem: An auto-rickshaw travels at 30 km/h. Neha’s school is 6 km from her home. How many minutes does the ride take?
Solution:
Step 1: Time = 6 ÷ 30 = 0.2 hours
Step 2: Convert: 0.2 × 60 = 12 minutes
Answer: The ride takes 12 minutes.
Example 8: Example 8: Walking Speed
Problem: Kavi walks at 5 km/h. He walks for 1 hour 30 minutes. How far does he walk?
Solution:
Step 1: Time = 1.5 hours (1 hour 30 min = 1.5 hours)
Step 2: Distance = 5 × 1.5 = 7.5 km
Answer: Kavi walks 7.5 km.
Example 9: Example 9: Conversion (km/h to m/s)
Problem: A bus travels at 72 km/h. Express this speed in m/s.
Solution:
Step 1: 1 km = 1,000 m. 1 hour = 3,600 seconds.
Step 2: 72 km/h = 72 × 1000 / 3600 = 72,000 / 3,600 = 20 m/s
Answer: The bus travels at 20 m/s.
Example 10: Example 10: Round Trip
Problem: Meera drives from her home to her grandmother’s house (90 km) at 45 km/h and returns at 30 km/h. Find the total time for the round trip.
Solution:
Step 1: Time going = 90 ÷ 45 = 2 hours
Step 2: Time returning = 90 ÷ 30 = 3 hours
Step 3: Total time = 2 + 3 = 5 hours
Answer: The total time is 5 hours.
Key Points to Remember
- Speed = Distance ÷ Time. Distance = Speed × Time. Time = Distance ÷ Speed.
- Speed is measured in km/h or m/s.
- Always ensure units are consistent (km with hours, or m with seconds).
- To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.
- For two-part journeys, calculate time for each part separately, then add.
- Average speed for a round trip is NOT the simple average of the two speeds.
- Convert minutes to hours: divide by 60. Convert hours to minutes: multiply by 60.
Practice Problems
- A bus covers 180 km in 3 hours. Find its speed.
- A cyclist rides at 15 km/h for 4 hours. How far does she ride?
- A train travels at 90 km/h. How long does it take to cover 450 km?
- Rahul runs 200 m in 40 seconds. What is his speed in m/s?
- A car travels 150 km at 50 km/h and then 100 km at 25 km/h. Find the total time.
- Convert 54 km/h to m/s.
- Aditi walks at 4 km/h. How far does she walk in 45 minutes?
- A train leaves at 9:00 AM and arrives at 1:30 PM covering 270 km. Find the average speed.
Frequently Asked Questions
Q1. What is speed?
Speed is the distance covered per unit of time. It tells how fast an object is moving. Speed = distance ÷ time.
Q2. What are the three formulas for speed, time, and distance?
Speed = Distance ÷ Time. Distance = Speed × Time. Time = Distance ÷ Speed. If you know any two, you can find the third.
Q3. What does km/h mean?
km/h stands for kilometres per hour. It means the number of kilometres covered in one hour. For example, 60 km/h means 60 kilometres every hour.
Q4. How do I convert km/h to m/s?
Multiply by 5/18. For example, 36 km/h = 36 × 5/18 = 10 m/s.
Q5. How do I convert minutes to hours?
Divide by 60. For example, 30 minutes = 30/60 = 0.5 hours. 45 minutes = 45/60 = 0.75 hours.
Q6. What is average speed?
Average speed = total distance ÷ total time. For a round trip at different speeds, add the total distances and divide by the total time.
Q7. Why must units be consistent?
If distance is in km and time is in hours, speed will be in km/h. Mixing km with seconds or metres with hours gives incorrect answers.
Q8. How do I find time when it is in hours and minutes?
If time is 2 hours 30 minutes, convert to 2.5 hours (30 min = 0.5 hours). Then use the formula.
Q9. Is this topic in the NCERT Class 5 syllabus?
Yes. Basic speed, time, and distance problems are introduced in the Time chapter of NCERT/CBSE Class 5 Maths.
