First slide

Relative motion based problems

Question

Two trains take 3 second to pass one another when going in opposite directions but only 2.5 second 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 the original speed is:

Easy

A

10 sec
B

12 sec
C

15 sec
D

18 sec

Solution

Let speeds and lengths be v₁, v₂, and l₁ l₂.
$\frac{l_{1} + l_{2}}{v_{1} + v_{2}} = 3 and \frac{l_{1} + l_{2}}{v_{1} + 1 .5 v_{2}} = 2 .5$
By solving above equations, $v_{1} = \frac{l_{1} + l_{2}}{5}$
and $v_{2} = \frac{l_{1} + l_{2}}{7 .5}$
Required time = $\frac{l_{1} + l_{2}}{v_{1} - v_{2}} = 15 s$

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