Question

Two identical trains take $3sec$ to pass one another when going in the opposite direction but only $2.5sec$ if the speed of one is increased by $50$. The time one would take to pass the other when going in the same direction at their original speed is

• A. $10sec$
• B. $12sec$
• C. $15sec$
• D. $18sec$

Answer 1

Answer: (C)

$15sec$

Both identical trains have speed of $x$and $y$ m/s and sum of their lengths be $D$
Thus, $t=\frac{D}{(x+y)}=3$
When speed of one is increased by 50%: $t=\frac{D}{(1.5x+y)}=2.5$
$3x+3y=3.75x+2.5y$
$0.5y=0.75x$
$y=1.5x$
$D=3(x+y)=3\left(2.5x\right)=7.5x$
Thus, time for train moving in same direction= $\frac{D}{(y-x)}=\frac{7.5x}{(1.5x-x)}=\frac{7.5}{0.5}=15s$