Question

A train overtakes two persons, walking in opposite directions. it crosses one with the speed of a km/hr in X hrs and another with a speed of b km/hr in Y hrs. length of the train is

Answer 1

This is what i could understand from the question.

Answer 2

Answer:

Required length of the train is $ab (\frac{x + y}{b - a} )$ km

Step-by-step explanation:

Given,a train overtakes two persons, walking in opposite directions.

It is also given the train crosses the first person with the speed of a km/hr in X hrs and crosses the second person with the speed of b km/hr in Y hrs.

Let length of train be L km.

and speed of the train be S km/hr.

We know if two object walk in opposite directions then

Time $= \frac{sum \: of \: their \: length}{sum \: of \: their \: speed}$

Here length of man is negligible

So we will only take length of train.

According to question,

$a = \frac{l}{x + s} ....(1)$ and $b = \frac{l}{y +s } ....(2)$

From equation (1) and (2),

$a(x + s) = b(y + s) \\ ax + as = by + bs \\ as - bs = ax - by \\ s(a - b) = ax - by \\ s = \frac{ax - by}{a - b}$

We are putting value of s in equation (1),

$a = \frac{l}{x + \frac{ax - by}{a - b} } \\ l = a \times (x + \frac{ax - by}{a - b} ) \\ l = a \times ( \frac{ax - bx + ax - by}{a - b} ) \\ l = ab (\frac{x + y}{b - a} )$

Required length of the train is $ab (\frac{x + y}{b - a} ) \: km$

This is a problem of Speed and Distance chapter,

Know more about speed and distance -

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