A man travels by bus for 20 hours and then by train for 5 hours. If the…
2023
A man travels by bus for 20 hours and then by train for 5 hours. If the average speed of the bus was 20 kmph and that of the entire journey was 24 kmph, what was the average speed of the train?
- A.
44 kmph
- B.
30 kmph
- C.
36 kmph
- D.
40 kmph
Show answer & explanation
Correct answer: D
Average speed for any journey (or any leg-combination of it) is defined as total distance divided by total time: Average speed = Total distance / Total time. When a multi-leg journey's overall average speed and duration are known but one leg's speed is unknown, first recover the TOTAL distance from the overall average and total time, then subtract the distance covered by every OTHER leg (found from ITS OWN speed and time) — the remainder is the unknown leg's distance, and dividing that by its own time gives its speed.
Total time for the journey = 20 hours (bus) + 5 hours (train) = 25 hours.
Total distance covered = average speed of the whole journey × total time = 24 × 25 = 600 km.
Distance covered by bus = bus's speed × bus's time = 20 × 20 = 400 km.
Distance covered by train = total distance − bus distance = 600 − 400 = 200 km.
Average speed of train = train distance ÷ train time = 200 ÷ 5 = 40 kmph.
Verify by re-combining: a 400 km leg at 20 kmph takes 20 hours and a 200 km leg at 40 kmph takes 5 hours, so total distance ÷ total time = 600 ÷ 25 = 24 kmph — matching the given overall average speed of the journey.