Question

The distance between Ahmedabad and Vadodara is $100$ km. Two trains set-off simultaneously from Ahmedabad and Vadodara towards each other. The speeds of these trains are $45$ km$h^{-1}$ and $30$ km $h^{-1}$ respectively. When will they cross each other?

Answer 1

Given distance between Ahmadabad and Vadodara =100 km

Velocity of train A $v_A$=45 km/hr and velocity of train B $v_B$=30 km/hr

Let the two trains meet at a distance x from their from A's origin.

Thus distance traveled by train A at time t =x km and distance traveled by train B at same time period of t =100 -x

Since the time function is same for both the trains we can equate for both the trains by the following expression

$\frac{x}{45}=\frac{100-x}{30}$

$30x=4500-45x$

$x=\frac{4500}{75}$

$x=60km$

Thus train A will meet train B after covering a distance of 60 km.