Gun fire and trains

[maihuna]

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

19.8
22.5
58.6
59.4
111.80

[maihuna]

any taker for this one!!!!!!

[Uri]

i think the answer is 59.4 kmph

the train has obviously travelled distance equal to what sound should have travelled in 30 seconds. and the train has covered this distance in 10 minutes.
in 30 seconds sound travels 330*30=9900m=9.9 km
in 10 minutes the train covers 9.9 km
so, in 1 hr the train covers 9.9*6 km= 59.4 km

waiting eagerly for the OA

[dmateer25]

Gunshot to travel to beginning point of train = 330 * 60 * 10.5 = 207,900 meters

Gunshot to travel to where train heard it= 330 * 60 * 10 = 198,000 meters

207900 – 198000 = 9900 meters the train traveled


9900 * (1/1000) = 9.9 km train traveled in 10 minutes

9.9/(1/6) = 59.4 km/hr

[maihuna]

yep correct oa is 59.4 only

[sureshbala]

If the train was at rest the second shot will be heard after 10 min 30 sec. But since the train is approaching the gun shot place, the second shot is heard after 10 min.

So the distance covered by train in 10 min will be covered by sound in 30 seconds.

Hence the speed of the train = (330 x 30)/10 mts/min = 990 mts/min

= 990 x 60 / 1000 km/hr = 59.4 km/hr.

I guess this is not from GMAT (must be from CAT). Also the units in GMAT exam will be miles/hr.