Question

Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of train (in km/hr), supposing that sound travels at 330 m/s is ?

Answer 1

Answer = 16.5 m/s = 59.4 kmph.
See the diagram.

Uniform Speed of the train = Vt m/s.
Speed of Sound = Vs m/s.

Let the first gun be fired at t = 0. At t = 0, let the train be at a distance d from the guns. Let the Second gun be fired at t= 630 sec.

Let the first gun shot be heard at t = t1 sec. Let the second gun shot be heard at t = (630+ t2) sec.

Short method:
Distance traveled by sound in 30 sec. (10.5 min - 10 min) = distance traveled by the train in 10 min.
30×Vs = 600 × Vt
So Vt = Vs/ 20 = 330/ 20= 16.5 m/s
Vt = 16.5 × 18/5 = 59.4 kmph.

See the diagram enclosed for detailed derivation and solution.