Bullets

[knight247]

Victor fires two bullets from the same place with an interval of 12 minutes between each bullet. Ron, sitting in a train approaching Victor, hears the sound of the second bullet 11 minutes and 30 seconds after he hears the sound of the first.

What is the speed of the train if the speed of sound is 330 m/s?

No OA. Detailed explanations would be appreciated. Thanks in advance.

[arjunbudhraja]

Here's a crude diagram to imagine the situation:

X -------------------->> <<--------------Y2--------Y1

X is the point from where the bullets were fired.
Y1 is the point where sound of first bullet was heard and Y2 is the point at which sound of second bullet was heard.

Since bullets were fired 12 minutes apart and the sounds were heard 11 minutes and 30 seconds apart, it means that the sound traveled from Y2 to Y1 in 30 seconds.
The sound of the second bullet would reach point Y1 in total of 12 minutes, just like the first bullet.

We need to find the distance between Y1 and Y2 in order to find the speed of the train. Total time taken by train to travel from Y1 to Y2 was 11 minutes and 30 seconds.

Distance traveled by the train to reach Y2 from Y1 = the distance the bullet will travel in the next 30 seconds to reach Y1 from Y2 = 30seconds * 330 m/s = 9900 metres.

Based on this, speed of the train = 9900 metres/ 11 minutes 30 seconds = 9900 m/ 690 s = 330/23 m/s