Question

A train travelling at 100 kmph overtakes a motorbike travelling at 64kmph in 40 sec. what is the length of the train in meter?

Answer 1

When two object moves in same direction then their relative speed is their difference.

Since we know that,
$speed = \frac{distance}{time}$
So,
$= > (100 - 64) \times \frac{5}{8} = \frac{distance}{40} \\ = > 36 \times \frac{5}{8} = \frac{d}{40} \\ = > 10 = \frac{d}{40}$
$= > distance = 400m$

Answer 2

Given:

Velocity of the train $=100kmph$

Velocity of motorbike $=64kmph$

Time $=40sec$

To find:

Length of the train

Solution:

$V_{train} =100$ × $\frac{5}{18}=27.8m/s$

$V_{bike} =64$ × $\frac{5}{18}=17.8m/s$

It is given that train overtakes bike in 40 seconds. Since, both train and bike are moving in the same direction, We understand that since the speed of the train is greater hence, after 40 seconds, train will be ahead of the bike.

Now,

Relative velocity of bike with respect to the train,

$V_{BT}=V_{T} -V_{B}$

$V_{BT}=27.8-(17.8)$

$V_{BT}=10m/s$

In the beginning of the overtake, let's assume the engine of the train and motorbike are at same starting point.

Now, since the train has some extra velocity which is $10m/s$ which is the factor helping train to overtake the motorbike in the given time according to the question that is $40 sec.$

The distance of the last compartment of the train from the bike is the length of the train.

Hence, distance covered by the distance covered by the last compartment of the train with $10m/s$ in $40sec$ is given by

$d=s$ × $t$

$d=10$ × $40$

$d=400m$

Final answer:

Hence, the length of the train is 400 m.