Train speed

Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is:

Correct result:

v =  61.2 km/h

Solution:

t1=(10+3060)/60=740=0.175 h t2=10/60=160.1667 h  t=t1t2=0.1750.166711200.0083 h v1=340 3.6=1224 km/h  t v1=t2 v  v=v1 tt2=1224 0.00830.1667=3065=61.2 km/ht_{1}=(10+\dfrac{ 30 }{ 60 } ) /60=\dfrac{ 7 }{ 40 }=0.175 \ \text{h} \ \\ t_{2}=10/60=\dfrac{ 1 }{ 6 } \doteq 0.1667 \ \text{h} \ \\ \ \\ t=t_{1}-t_{2}=0.175-0.1667 \doteq \dfrac{ 1 }{ 120 } \doteq 0.0083 \ \text{h} \ \\ v_{1}=340 \cdot \ 3.6=1224 \ \text{km/h} \ \\ \ \\ t \cdot \ v_{1}=t_{2} \cdot \ v \ \\ \ \\ v=v_{1} \cdot \ \dfrac{ t }{ t_{2} }=1224 \cdot \ \dfrac{ 0.0083 }{ 0.1667 }=\dfrac{ 306 }{ 5 }=61.2 \ \text{km/h}



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