Two trains A and B are running in opposite directions with different speeds. The speed of train B is 18 km/h more than that of A. Train A crosses a pole in 32 seconds and its length is 210 m less than that of train B. If they cross each other in 34 seconds, the length of train A is ________.

Given:

Speed of train B is 18km/h more than that of train A.

Length of train A is 210m less than that of train B.

Calculation:

Let D is the length of train A and the speed of train A be x m/s.

Then length of train B = D + 210

And the speed of train B is 18 km/h(18 × 5/18 = 5 m/s) more than the speed of train A.

Speed of train B = (x + 5) m/s

Train A crosses a pole in 32 seconds,

32 = D/x

⇒ x = D/32  ...... (i)

Both trains cross each other in 34 seconds

34 = (D + D + 210)/(x + x + 5) = (2D + 210)/(2x+5)

From (i),

⇒ 34 = (2D + 210)/(2 × D/32 +5)

⇒ 34 = (2D + 210)/(D/16 + 5)

⇒ 34 × (D/16 + 5) = 2D + 210

⇒ 34D + 16 × 170 = 32D +  16 × 210

⇒ 34D - 32D = 16 × 210 - 16 × 170

⇒ 2D = 16 × 40

⇒ D = 320 m.