Question

The time taken by two running trains in crossing each other is calculated by dividing the sum of the lengths of two trains by the total speed of the two trains. If the length of the first train is $L_1$, the length of the second train is $L_2$, the speed of the first train is $V_1$ and the speed of the second train is $V_2$, which of the following expressions would represent the time taken?

• A. $\left(L_1^{\prime \prime }{L}_2\right)\ast \left(V_1^{\prime \prime }{V}_2\right)$
• B. $\left(L_1^{\prime \prime }{L}_2\right)@(V_1"V_2)$
• C. $\left[\right(L_1"L_2\left)@\right(V_1"V_2\left)\right]\ast 60$
• D. $\left(L_1^{\prime }{L}_2\right)@\left(V_1^{\prime }{V}_2\right)$

Answer 1

The correct option is B $\left(L_1^{\prime \prime }{L}_2\right)@(V_1"V_2)$

Clearly, time taken $=\frac{\text{sum of lengths of two trains}}{\text{total speed of two trains}}$
$=\frac{L_1+L_2}{V_1+V_2}=(L_1"L_2)@(V_1"V_2)$