A train normally covers a certain distance at a speed of 100 km/hr. If it…
2024
A train normally covers a certain distance at a speed of 100 km/hr. If it halts for a fixed time interval in each hour, its average speed reduces to 80 km/hr. What is the average time interval for which the train halts in each hour?
Answer: B. 12 minutes — Approach: model the halt time per hour and compute the average speed. Let the train halt for h minutes each hour. Then the train runs for (60 − h) minutes in…
- A.
10 minutes
- B.
12 minutes
- C.
15 minutes
- D.
20 minutes
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Correct answer: B
Approach: model the halt time per hour and compute the average speed.
Let the train halt for h minutes each hour. Then the train runs for (60 − h) minutes in each real hour.
Distance covered in one real hour = speed while running × running time (in hours) = 100 × (60 − h)/60 km.
This average distance per hour equals the given average speed 80 km/hr, so 100 × (60 − h)/60 = 80.
Solve for h: (60 − h)/60 = 0.8 ⇒ 60 − h = 48 ⇒ h = 12 minutes.
Answer: 12 minutes