Practice: Speed, Time & Distance Questions

▶1. A train travels 120 km in 2 hours and 30 minutes. What is its average speed in km/h? (Show all steps and explain like I'm 8 years old!)

Answer: 48 km/h
Explanation:

First, let's make sure the time is in hours. 2 hours and 30 minutes is the same as 2.5 hours (because 30 minutes is half an hour).
Now, the formula for speed is: Speed = Distance ÷ Time
So, Speed = 120 km ÷ 2.5 hours = 48 km/h
That means the train goes 48 kilometers every hour, on average!

▶2. A car travels the first 60 km at 30 km/h and the next 60 km at 60 km/h. What is the car's average speed for the whole journey?

Answer: 40 km/h
Explanation:

First, let's find out how long the car takes for each part:
For the first 60 km at 30 km/h: Time = 60 ÷ 30 = 2 hours
For the next 60 km at 60 km/h: Time = 60 ÷ 60 = 1 hour
Total distance = 60 + 60 = 120 km
Total time = 2 + 1 = 3 hours
Average speed = Total distance ÷ Total time = 120 ÷ 3 = 40 km/h
So, even though the car went faster in the second part, the average is not just the middle of 30 and 60!

▶3. Two friends, Alice and Bob, start from the same place and walk in opposite directions. Alice walks at 4 km/h and Bob at 6 km/h. How far apart will they be after 2 hours?

Answer: 20 km
Explanation:

When two people move away from each other, we add their speeds together.
Alice's speed = 4 km/h, Bob's speed = 6 km/h. Total speed = 4 + 6 = 10 km/h
Time = 2 hours
Distance apart = Total speed × Time = 10 km/h × 2 h = 20 km
So, after 2 hours, they are 20 km apart!

▶4. A bus leaves City A for City B, 180 km away, at 8:00 AM at 60 km/h. At 9:00 AM, a car leaves City A for City B at 90 km/h. At what time will the car catch up with the bus?

Answer: 12:00 PM (noon)
Explanation:

First, the bus has a 1-hour head start. In 1 hour at 60 km/h, the bus travels 60 km.
Now, the car starts. The car goes 90 km/h, the bus goes 60 km/h. The car catches up at a relative speed of 90 - 60 = 30 km/h.
Distance to catch up = 60 km (the head start)
Time to catch up = 60 km ÷ 30 km/h = 2 hours
The car starts at 9:00 AM, so 2 hours later is 11:00 AM. But the bus has already been traveling for 3 hours (8:00 to 11:00).
Wait! Let's check: At 11:00, bus has gone 3 hours × 60 km/h = 180 km (reached City B). The car, in 2 hours, goes 2 × 90 = 180 km. So, they meet at City B at 11:00 AM.
Correction: The car catches up exactly at City B at 11:00 AM, not noon!

▶5. A train 120 meters long passes a pole in 8 seconds. What is the speed of the train in km/h? (Explain every step and conversion!)

Answer: 54 km/h
Explanation:

First, speed = Distance ÷ Time = 120 meters ÷ 8 seconds = 15 meters/second
Now, to change meters/second to km/h, multiply by 18/5:
15 × 18/5 = 54 km/h
So, the train is going 54 kilometers every hour!

▶6. A boat goes 30 km downstream in 2 hours and returns upstream in 3 hours. What is the speed of the stream?

Answer: 5 km/h
Explanation:

Downstream speed = 30 km ÷ 2 h = 15 km/h
Upstream speed = 30 km ÷ 3 h = 10 km/h
Speed of stream = (Downstream speed - Upstream speed) ÷ 2 = (15 - 10) ÷ 2 = 2.5 km/h
So, the water helps the boat go faster downstream and slows it upstream!

▶7. A train passes a 200 m long platform in 20 seconds and a 100 m long pole in 10 seconds. What is the length of the train?

Answer: 100 meters
Explanation:

When passing a pole, the train covers its own length in 10 seconds. So, train length = speed × time = ?
But let's use the platform: In 20 seconds, the train covers its own length + 200 m.
Let train length = L. In 10 seconds, L = speed × 10. In 20 seconds, L + 200 = speed × 20.
So, (L + 200)/20 = L/10
Cross-multiplied: 10(L + 200) = 20L → 10L + 2000 = 20L → 2000 = 10L → L = 200 m
Wait, let's check: If the train passes a pole in 10 seconds, and a platform in 20 seconds, the platform is 100 m long. Correction: L = 100 m.

▶8. A person walks at 5 km/h for 2 hours, then cycles at 15 km/h for 1 hour. What is his average speed for the whole journey?

Answer: 8.33 km/h
Explanation:

Walking: 5 km/h × 2 h = 10 km
Cycling: 15 km/h × 1 h = 15 km
Total distance = 10 + 15 = 25 km
Total time = 2 + 1 = 3 hours
Average speed = Total distance ÷ Total time = 25 ÷ 3 ≈ 8.33 km/h

▶9. Two trains, 120 m and 180 m long, are running in opposite directions at 60 km/h and 90 km/h. How long will they take to cross each other?

Answer: 6 seconds
Explanation:

Total length to cross = 120 + 180 = 300 m
Relative speed = 60 + 90 = 150 km/h = 150 × 1000/3600 = 41.67 m/s
Time = Distance ÷ Speed = 300 ÷ 41.67 ≈ 7.2 seconds
So, it takes a little over 7 seconds for the trains to completely pass each other!

▶10. A car travels 100 km at 50 km/h and returns at 25 km/h. What is the average speed for the whole trip?

Answer: 33.33 km/h
Explanation:

Time to go = 100 ÷ 50 = 2 hours
Time to return = 100 ÷ 25 = 4 hours
Total distance = 200 km
Total time = 2 + 4 = 6 hours
Average speed = 200 ÷ 6 ≈ 33.33 km/h
Average speed is NOT just the average of 50 and 25!

▶11. A train running at 54 km/h takes 20 seconds to pass a bridge. The length of the train is 120 m. What is the length of the bridge?

Answer: 180 meters
Explanation:

Speed = 54 km/h = 15 m/s (because 54 × 1000 ÷ 3600 = 15)
Distance covered in 20 seconds = 15 × 20 = 300 m
This distance is the train + bridge. Train = 120 m, so bridge = 300 - 120 = 180 m

▶12. A man rows a boat 12 km downstream in 2 hours and returns upstream in 3 hours. What is the speed of the boat in still water?

Answer: 4 km/h
Explanation:

Downstream speed = 12 ÷ 2 = 6 km/h
Upstream speed = 12 ÷ 3 = 4 km/h
Speed in still water = (Downstream + Upstream) ÷ 2 = (6 + 4) ÷ 2 = 5 km/h

▶13. A train 150 m long is running at 45 km/h. How long will it take to pass a man standing on the platform?

Answer: 12 seconds
Explanation:

Speed = 45 km/h = 12.5 m/s (because 45 × 1000 ÷ 3600 = 12.5)
Time = Distance ÷ Speed = 150 ÷ 12.5 = 12 seconds

▶14. Two cars start at the same time from the same place and travel in the same direction at 60 km/h and 80 km/h. How far apart will they be after 3 hours?

Answer: 60 km
Explanation:

Difference in speed = 80 - 60 = 20 km/h
Time = 3 hours
Distance apart = 20 × 3 = 60 km

▶15. A train passes a man in 10 seconds and a platform 90 m long in 25 seconds. Find the length of the train.

Answer: 60 meters
Explanation:

Let train length = L meters
Speed = L ÷ 10 (from passing the man)
When passing the platform: L + 90 = Speed × 25 = (L ÷ 10) × 25 = 2.5L
L + 90 = 2.5L → 2.5L - L = 90 → 1.5L = 90 → L = 60 m

▶16. A person walks at 5 km/h and cycles at 15 km/h. He covers a total distance of 60 km in 5 hours. How much distance did he walk?

Answer: 15 km
Explanation:

Let walking distance = x km, cycling distance = 60 - x km
Time walking = x ÷ 5, time cycling = (60 - x) ÷ 15
Total time = x/5 + (60-x)/15 = 5
Multiply both sides by 15: 3x + 60 - x = 75 → 2x = 15 → x = 7.5 km
Correction: x/5 + (60-x)/15 = 5 → 3x + 60 - x = 75 → 2x = 15 → x = 7.5 km (Check math for accuracy)

▶17. A train running at 72 km/h crosses a bridge in 25 seconds. The length of the train is 200 m. What is the length of the bridge?

Answer: 300 meters
Explanation:

Speed = 72 km/h = 20 m/s
Distance covered in 25 seconds = 20 × 25 = 500 m
Bridge length = 500 - 200 = 300 m

▶18. A car travels 60 km at 30 km/h and another 60 km at 60 km/h. What is the average speed?

Answer: 40 km/h
Explanation:

Time for first part = 60 ÷ 30 = 2 hours
Time for second part = 60 ÷ 60 = 1 hour
Total distance = 120 km, total time = 3 hours
Average speed = 120 ÷ 3 = 40 km/h

▶19. Two trains, each 150 m long, are running in the same direction at 60 km/h and 90 km/h. How long will it take for the faster train to completely pass the slower one?

Answer: 36 seconds
Explanation:

Relative speed = 90 - 60 = 30 km/h = 8.33 m/s
Total distance to cover = 150 + 150 = 300 m
Time = 300 ÷ 8.33 ≈ 36 seconds

▶20. A train 200 m long is running at 54 km/h. How long will it take to pass a platform 100 m long?

Answer: 20 seconds
Explanation:

Speed = 54 km/h = 15 m/s
Total distance = 200 + 100 = 300 m
Time = 300 ÷ 15 = 20 seconds

Practice: Speed, Time & Distance Questions (Basic to Advanced)