# What will be the length of slower train?

when two trains were running in the same direction at 90 km/hr and 70 km/hr then the fastest train passed a man sitting in the slow train in 36 seconds. What is the length of the fastest train?

Ans I found as per answer provided in the book as 200 meters.

i.e (90-70)36(5/18) = 200 meters

then what will be the speed of slower train? As question never tells us that both are of same length.. So how to calculate?

• 70 km/h???????? – kiss my armpit Dec 14 '13 at 13:12
• @StiffJokes: 70 km/hr means? – Rasmi Ranjan Nayak Dec 14 '13 at 13:16
• "what will be the speed of slower train" – peterwhy Dec 14 '13 at 13:16
• According to Newton's first law, the speed will be constant if no external force. – kiss my armpit Dec 14 '13 at 13:17
• So if special relativity is necessary, then the question is no longer (linear-algebra)? :P – peterwhy Dec 14 '13 at 13:21

From the reference of the Earth, the speeds of trains are $90$ km/h and $70$ km/h respectively. Then the distance of faster train travelled is

$$\text{Distance} = \text{speed}\times\text{time}\\ (90/3.6)\times36 = 900\text{ m}$$

and the distance that the slower train travelled is $$(70/3.6)\times36 = 700\text{ m}$$

The difference, $200$ m, would be the length of the faster train.

The speed of the slower train is $70$ km/h as given.

It doesn't matter what length the slow train is, because you are only looking at a specific point on it. In fact, you can look at this problem as "Given a fast train moving 90 km/hr, say it takes 36 seconds to pass a man moving 70 km/hr in the same direction."

Which is an easy Distance = Rate X Time, where distance is your length (because once the front of the train is level with the man, then it most go one train length to pass the man), rate is just the difference between the two speeds, and time is of course time.