Two guns were fired from the same place at an interval of 20 minutes but a person in a train approaching the place hears the sound 16 minutes 30 seconds after the first. Find the speed of the train (in kmph) supposing that the sound travels 330 meters per second.

Solution

The distance travelled by the train in 16min 30 seconds will be equal to that travelled by sound (20 min – 16 min 30 sec) = 3 min 30 seconds The train travelled 330 × 210 meters in 16 1/2 minutes. ∴ Speed of the train per hour = (330 × 210 × 2 × 60)/(33 ×1000) = 252 km/hr ALTERNATE METHOD: Let speed of train = x m/s The distance covered by bullet with a speed of sound 330m/s in 20 minutes is equal to distance covered by train & bullet together in 16 min 30 sec So let speed of train = x m/s So 330 × 20 = (x+330) × 16 ×1/2 6600 × 2/33 = x + 330 So x + 330 = 400 Or x = 70 m/s = 70 × 18/5 kmph = 252kmph