Question

A train 150 m long passes a km stone in 15 seconds and another train of the same length travelling in opposite direction in 8 seconds.The speed of the second train is
a)60 kmph b)66 kmph c)72 kmph d)99 kmph

Answer 1

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Distance = 150m + 1km
= 0.150 +1
= 1.15 km
Time = 8 sec
$= \frac{8}{60 \times 60} hrs$
Speed of second train is = Distance/Time
$= \frac{1.15}{ \frac{8}{60 \times 60} } \\ = \frac{1.15 \times 60 \times 60}{8} \\ = 517.5 \: km \: per \: hour$

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Answer 2

Formula:

Speed =$\frac{Distance}{Time}\\ \\ Given:\\ \\ Length_{first\ train} (L_1)= Length_{second\ train} (L_2)\\ \\ L_2 = 150m$

Solution:

$Speed_{second train}\ (S_2)=\frac{150}{15} = 10 m/sec$

Let $S_2$ be x m/sec  

Relative speed = 10 + x ($Speed_{first\ train}+Speed_{second\ train}$ )  

Length of both the trains = Relative speed× time  

Relative speed =$\frac{Length\ of\ both\ the\ trains}{time}$  

$\frac{300}{10} + x = 8$  

300 = 8(10 + x)  

300 = 80 + 8x  

8x = 220  $x =\frac{55}{2}m/sec$

$1 m/sec =\frac{18}{5} kmph$

$S_2 =\frac{55}{2} *\frac{18}{5} kmph$

∴$Speed_{second\ train}= 99 kmph$