Question

Two train each of length $50m$ are running with constant speeds on parallel tracks while moving in same direction one over takes the other in $40$ seconds and while moving in opposite direction one crosses the other in $20$ seconds. The speeds of trains will be

• A. $2.25m{s}^{-1}$ and $2.75m{s}^{-1}$
• B. $2.15m{s}^{-1}$ and $2.85m{s}^{-1}$
• C. $3.75m{s}^{-1}$ and $1.25m{s}^{-1}$
• D. $4.25m{s}^{-1}$and $0.75m{s}^{-1}$

Answer 1

The correct option is C $3.75m{s}^{-1}$ and $1.25m{s}^{-1}$

Let the speeds be $v_1$ and $v_2$. While moving in same direction, relative speed $=v_1-v_2$, and in opposite direction, it is $v_1+v_2$.
Thus, we have $Dis{t}_{rel}=v_{rel}\times t$
$2\times 50=40(v_1-v_2)=20(v_1+v_2)$
or, $v_1-v_2=2.5$ and $v_1+v_2=5$
solving them, we have, $v_1=3.75$ and $v_2=1.25$