Question

A train overtakes two persons who are walking in the same direction in which the train is going, at the rate of 2 kmph and 4 kmph and passes them completely in 9 and 10 seconds respectively. The length of the train is:??

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Answer 1

Answer:

50m.

Step-by-step explanation:

It is given that the speed of the two persons who are walking in the same direction in which the train is going at the rate of 2 kmph and 4 kmph.

Firstly we will convert the given speed of the two persons from kmph to m/s.

Speed of first person = 2kmph = 2 × 5/18m/s

= 59m/s

Now, Speed of second person

= 4kmph = 4 × 5/18m/s = 9/10m/s

Also, it is given that the train passes them completely in 9 and 10 seconds.

We know that ratio of the distance to the speed is equals to the time.

$\frac{distance}{speeed} = time$

Let x meters be the length of the train and y m/s be the speed of the train.

Substituting the values in above equation,

we get,

⇒x/(y−5/9) = 9sec

Simplifying the equation, we get

⇒9y−5=x

We will multiply both sides by 10.

Therefore the equation becomes,

⇒90y−50=10x……………… (1)

Time taken by train to cross second person =10sec

⇒distance/speed=10sec

⇒xy−109=10sec

Simplifying the equation, we get

⇒90y−100=9x………………(2)

Now we will subtract equation (2)

from the equation (1) to get the value of x. Therefore, we get

⇒(90y−50)−(90y−100)=10x−9x

Rewriting the above equation, we get

⇒90y−50−90y+100=x

Adding and subtracting the like terms, we get

⇒x=50m

Hence, the length of the train is 50m.