Question

Two trains travel in opposite directions at $36km/hr$ and $45km/hr$ respectively. A man sitting in the slower train passes the faster train in $8sec$. What will be the length of the faster train $?$

• A. $80m$
• B. $120m$
• C. $150m$
• D. $180m$

Answer 1

The correct option is D

$180m$

Finding the length of the faster train :

Let the length of the faster train be $lm$.

Now, the trains are moving in the opposite direction. So, we know that when the trains in opposite direction we add the speed of both the bodies.

Relative speed $\begin{array}{rcl}& =& 36+45\end{array}$

$\begin{array}{rcl}& & \\ & =& 81km/hr\\ & =& 81\times \frac{5}{18}\\ & =& \frac{45}{2}m/s\end{array}$

Now, we know that

$$\begin{gathered} \mathrm{Speed}=\frac{\mathrm{distance}}{\mathrm{time}} \\ \mathrm{Distance}=\mathrm{speed}\times \mathrm{time} \\ \mathrm{l}=\frac{45}{2}\times 8 \\ \mathrm{l}=180\mathrm{m} \end{gathered}$$

Hence, option D is correct.