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(A) Let the speed of the train be $v_t 	ext{ m/s}$.The time interval between the two gunshots is $13 	ext{ minutes} = 780 	ext{ seconds}$.The time

Vedclass · Accepted Answer

$47 \frac{13}{25}$

Vedclass · Answer

(A) Let the speed of the train be $v_t 	ext{ m/s}$.The time interval between the two gunshots is $13 	ext{ minutes} = 780 	ext{ seconds}$.The time interval at which the person hears the shots is $12 	ext{ minutes } 30 	ext{ seconds} = 750 	ext{ seconds}$.In the time the train travels for $750 	ext{ seconds}$,the sound of the second shot covers the distance that the train would have covered in the remaining $30 	ext{ seconds}$ $(780 - 750 = 30 	ext{ seconds})$.Distance covered by sound in $30 	ext{ seconds} = 330 	imes 30 = 9900 	ext{ meters}$.This distance is covered by the train in $750 	ext{ seconds}$.Speed of the train $v_t = \frac{9900}{750} 	ext{ m/s} = 13.2 	ext{ m/s}$.To convert $	ext{m/s}$ to $	ext{km/hr}$,multiply by $\frac{18}{5}$:$v_t = 13.2 	imes \frac{18}{5} = \frac{132}{10} 	imes \frac{18}{5} = \frac{2376}{50} = \frac{1188}{25} 	ext{ km/hr}$.$v_t = 47 \frac{13}{25} 	ext{ km/hr}$.

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