Question

A running train crosses a man standing in the platform in 9 sec and a bridge 360 m long in 21 sec.Find the speed of the train and length of the train

Answer 1

Answer:

30 m/s and 270 m

Explanation:

Let

• Speed of train = v
• Length of train = x

In first case while crossing the man

Speed = Distance / Time

v = x/9 .....(1)

In second case while crossing the the bridge of 360 m

Speed = Distance / Time

v = (360 + x) / 21 .....(2)

Equate equations (1) and (2)

x/9 = (360 + x)/21

21x = 3240 + 9x

12x = 3240

x = 3240 / 12

x = 270 m

Now, from equation (1)

v = x/9

= 270/9

= 30 m/s

Answer 2

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Let say the speed of train to be v

Let's at the length of train to be x

Now we have been given that :-

• In first case :-

1. Time taken to cross man = 9s
2. Distance travelled in crossing man = x
3. Speed there = v

Thus I'm first case : v = x /9 ---1

Now in second case we have been given that :-

• Time taken to cross bridge = 21d
• Distance travelled in crossing bridge = 360m
• Speed at this instant = v

Thus we can say that in second case

v = 360 / 21 ---2

Now the total distance travelled in journey will be 360 + x

On equating both eq 1 and eq 2 we get :-

$\frac{x}{9} = 3240 + 9x$

$21x = 3240 + 9x$

$21x - 9x = 3240$

$12x = 3240$

$x = \frac{3240}{12}$

$x = \cancel \frac{3240}{12}$

$x = 270m$

Therefore the length of train is 270m.

Now after inputting this value in equation 1 we get :-

$v = \frac{x}{9}$

$v = \frac{270}{9}$

$v = 30 \frac{m}{s}$

Therefore the speed of bus is 30m/s.

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BY SCIVIBHANSHU

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