Question

Two trains A and B start from Delhi and Kolkata towards
Kolkata and Delhi respectively. After passing each other,
they take 10 hours and 2 hours 30 minutes respectively
to reach their destinations. If Train A is moving at the
speed of 37.5 kmh", what is the speed of Train B?

Answer 1

Let s = speed of train B
Let t = elapsed time before the trains pass
Closing speed of the two trains = 37.5 + s
Distance travelled at the closing speed = t(37,5 + s) = 37.5t + st
This distance also equals the total distance between the cities = 2.5s + 375
Therefore 37.5t + st = 2.5s + 375 ..................(1)
Also st = 375 giving
s = 375/t ........................................................(2)
Substituting the value for s found in (2) into equation (2) gives
37.5t + 375 = (2.5 * 375)/t + 375
Therefore\[37.5t=\frac{2.5\times 375}{t}\]
\[t ^{2}=\frac{2.5\times 375}{37.5}=\sqrt{25}=5\ hours\]
So train B travels 375 km in 5 hours giving the speed of train B to be 375/5 = 75 km/hr