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
The distance travelled by train A after passing train B = 37.5 * 10 = 375 km
Let t = the time taken before the trains pass.
Distance travelled by train B before the trains pass = st =375 km
Therefore s = 375/t .........................................(1)
The closing speed of the trains = 37.5 + s
Total distance travelled by trains before passing = 375 + 2.5s
\[time=\frac{distance}{speed}\]
\[t=\frac{375+2.5s}{37.5+s}\]
which gives
\[37.5t+st=375+2.5s .................(2)\]
Substituting the value for s from (1) into (2) gives
\[37.5t+375=375+\frac{2.5\times 375}{t}\]
which simplifies to
\[37.5t=\frac{2.5\times 375}{t}\ .........................(3)\]
Rearranging (3) we get\[t=\sqrt{\frac{2.5\times 375}{37.5}}\]
Speed of train B = 375/t