Question

A train $100m$ long traveling at $40m{s}^{-1}$ starts overtaking another train $200m$ long traveling at $30m{s}^{-1}$. Find the time taken by the first train to pass the second train completely.

Answer 1

Step 1: Given

Length of $1^{st}$ train = $100m$

Length of $2^{nd}$train = $200m$

Speed of $1^{st}$train = $40m{s}^{-1}$

Speed of $2^{nd}$train = $30m{s}^{-1}$

Step 2: Formula used and calculation of time

Since both trains are moving the concept of relative speed will be used.

Since both trains are moving in the same direction, relative speed will be the difference between their speeds.

So, the relative speed $v=40m{s}^{-1}-30m{s}^{-1}=10m{s}^{-1}$

Total distance to be covered, $d=100m+200m=300m$

Time taken to overtake is given by

$$\begin{gathered} t=\frac{dis\tan ce\left(d\right)}{speed\left(v\right)} \\ =\frac{300m}{10m{s}^{-1}} \\ =30s \end{gathered}$$

Hence, $1^{st}$ train will take $30s$ to overtake the $2^{nd}$train.