A train overtakes two persons walking along a railway bridge. The first one walks at 4 km/h and the other one walks at 6 km/h. The train needs 4.2 and 4.8 seconds, respectively, to overtake them. What is the speed of the train, if both the persons are walking in the same direction?
Solution
Let the speed of the train be x km/h.
The resultant speed of the train with respect to the first person shall be (x-4) km/h, and that for the second person is (x-6) km/h.
In 4.2 seconds, the train overtakes the first person. Hence, the distance between them is $$\frac{\ 4.2}{3600}\times\ \left(x-4\right)$$
In 4.8 seconds, the train overtakes the first person. Hence, the distance between them is $$\frac{\ 4.8}{3600}\times\ \left(x-6\right)$$
These two values are equal. From this, we get x= 20 km/h.
