Train ‘P’, running with a speed of 144 km/h, crosses a pole in 17 seconds. If the time taken by train ‘P’ to cross train ‘Q’ running with a speed of 72 km/h and coming from the opposite direction is 22.8 seconds, then find the length of train 'Q'.

Train P crosses a pole in 17 seconds. The length of Train P is equal to the distance it covers in 17 seconds.

Speed of Train P = 144 km/h

Convert speed to m/s:

144 × 5/18 = 40 m/s

Length of Train P = Speed × Time

Length of Train P = 40 × 17 = 680 m

Train P and Train Q are moving in opposite directions. Their relative speed is the sum of their individual speeds.

Speed of Train P = 144 km/h = 40 m/s

Speed of Train Q = 72 km/h

Convert speed to m/s:

72 × 5/18 = 20 m/s

Relative speed = 40 + 20 = 60 m/s 

Train P takes 22.8 seconds to cross Train Q. The combined length of the two trains is equal to the distance covered at the relative speed in 22.8 seconds.

Combined Length = Relative Speed × Time = 60 × 22.8 = 1368 m

The combined length of Trains P and Q is 1368 m, and the length of Train P is 680 m. Therefore, the length of Train Q is:

Length of Train Q = Combined Length Length of Train P = 1368 - 680 = 688 m

Thus, the length of Train Q is 688 meters.