I was just going through the explanations, but what I dont understand is that if the shot was fired 10.5 mins after the first one, how can the man hear the second shot even before it was shot!

Bunuel wrote:

Is this question too tough for GMAT level? or it can be considered for GMAT? I took 4 minutes to solve this.

Two guns were fired from the same place at an interval of 10 minustes 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 330m/s is:

a) 19.8

b) 58.6

c) 59.4

d) 111.8

Do let me know how log does it take for you and also if this is worth getting in GMAT.

In 30 sec sound covers the same distance as train in 10 min.

In 30 seconds sound covers 330*30=9900m=9.9 km, --> hence in 10 minutes train covers 9.9 km --> in 1 hr train covers 9.9*6 km= 59.4 km.

Answer: C.

I guess for GMAT it's 700+ question.[/quote]

Hi Bunuel, could you please explain more about the way you think this problem.

Thanks![/quote]

If the person were static he would hear ("meet") the sound in 10.5 minutes, but he heard ("met") the sound in 10 minutes, and that's because during these 10 minutes the person was moving towards the sound. Thus these 10 minutes of person moving "saved" the sound its 0.5 minutes of moving.

OR: let's say (imagine) the distance between the shooting point and person when the second shot was made was \(d\). We are told that this distance would be covered in 10.5 minutes if person were static: \(d=10.5s\) (\(s\) speed of sound).

But because person was was moving towards the sound they "met" in 10 minutes, which means that the distance \(d\) was covered in 10 minutes at their combined speed. Their combined speed was \(s+t\) (\(t\) the speed of person/train): \(d=10(s+t)\).

\(d=10.5s=10(s+t)\) --> \(0.5s=10t\).

Hope it helps.[/quote]