Question

A train travelling at a constant speed crosses a man cycling in the same direction at 18 km/h in 15 seconds and another motorbike in the same direction travelling at 36 km/h in 20 seconds. Find the speed of the train?

1. 100 km/h
2. 90 km/h
3. 110 km/h
4. 75 km/h

Answer 1

Correct Answer - Option 2 : 90 km/h

Given:

Speed of cycle = 18 km/h

Speed of motorbike = 34 km/h

Time taken to overtake cycle = 15 seconds

Time taken to overtake bike = 20 seconds

Formula used:

Km/h to m/s conversion - Multiply with 5/18

m/s to km/h conversion - Multiply with 18/5

Speed = Distance/Time

Calculation:

∵ 18 km/h = (5/18) × 18 = 5 m/s

36 km/h = (5/18) × 36 = 10 m/s

Let the length of the train = x mts

Speed of the train = y m/s

∴ Relative speed of the train w.r.t cycle = (y - 5) m/s

Relative speed of the train w.r.t bike = (y - 10) m/s

∴ (y - 5) × 15 = (y - 10) × 20

⇒ 15y - 75 = 20y - 200

⇒ 5y = 125

⇒ y = 25 m/s

∴ Speed of train in km/h = [25 × (18/5)] km/h

= 90 km/h