Question

Two guns were fired from the same place at an interval of 13 minutes but a person in a train approaching the place hears the second report 12 minutes 30 seconds after the first .Find the speed of the train ,supposing that sound travels at 330 metres per second.

Answer 1

13(330)60= 257400 m
is the distance moved by sound of bullet
Observer moving at speed of v records after 750 seconds
750*(330+v)=257400
330+v=343.2
v=13.2 m/s
 

Answer 2

The speed of the train is 47.52 km/hr.

Given:

Two guns fired at a time interval of 13 minutes at same place.

A person in a train hears the second shot "12 minutes 30 seconds" after the first shot.

To find:

The speed of the train by taking the speed of the sound as 330 meters per second  

Solution:

$In \ 12 \ minutes \ and \ 30 \ seconds \ (750 \ seconds), \ the \ train \ traveled \ distance = x$

$The \ distance \ travelled \ by \ the \ sound \ in \ 30 \ seconds =30 \times 330=9900 \ \mathrm{m} / \mathrm{s}$

$Speed \ of \ the \ train =\frac{9900}{750}$

$\Rightarrow \text { Speed of the train }=\frac{66}{5} \ \mathrm{m} / \mathrm{s}$

On converting m/s to km/hr, we get,

$\Rightarrow \text { Train speed }=\frac{66}{5} \times \frac{18}{5}$

$=\frac{1188}{25}$

$\therefore \text { Train speed }=47.52 \ \mathrm{km} / \mathrm{hr}$