A train traveling at the speed of x km/h crossed a 400 m long platform in 36 seconds and overtook a man walking in the same direction at the speed of 5 km/h in 18 seconds.  What is the value of x?

75

Let the length of train = L

Speed of train =x km/hr or x × \(\frac{5}{18}\) m/sec

For platform:

Total distance traveled by train in 36 sec = (L + 400) = {x × \(\frac{5}{18}\)} × 36

L = 10x - 400

For man:

Total distance traveled by train in 18 sec = L

Relative speed = (x - 5) km/hr or (x - 5) × \(\frac{5}{18}\) m/sec

L = {(x - 5) × \(\frac{5}{18}\)} × 18

L = (x - 5) × 5

Length of train is equal in both conditions, so:

(x - 5) × 5 = 10x - 400

5x - 25 = 10x - 400

5x = 375

x = 75 km/h