Question

A train 108 m long is moving at a speed of \[50\dfrac{km}{hr}\] . It crosses a train 112 m long coming from the opposite direction in 6 seconds. What is the speed of the second train?
(a) \[48\dfrac{km}{hr}\]
(b) \[54\dfrac{km}{hr}\]
(c) \[66\dfrac{km}{hr}\]
(d) \[82\dfrac{km}{hr}\]

Answer 1

Hint: We will first find relative speed of train by using the formula \[\text{Relative speed=}\dfrac{\text{total distance}}{\text{time taken}}\] where total distance is \[d=108+112=220m\] and time is 6 seconds. After this, we will convert the answer into \[\dfrac{km}{hr}\] by multiplying it with \[\dfrac{18}{5}\] . Then we know that relative speed is equal to speed of both the trains. Thus, putting the values in speed of\[\text{train1+train2=relative speed}\] and on solving, we will get our answer.

Complete step-by-step answer:
Here, we are given the speed of train1 i.e. \[50\dfrac{km}{hr}\] . Length of two train which we can consider as total distance is given i.e. \[d=108+112=220m\] . Time taken is given which is 6 seconds.
So, from this given data we will find out relative speed of train i.e. total speed using the formula \[\text{Relative speed=}\dfrac{\text{total distance}}{\text{time taken}}\] .
On substituting the values in the formula, we will get as,
 \[\text{Relative speed=}\dfrac{220}{6}=\dfrac{110}{3}\dfrac{m}{s}\]
We will convert \[\dfrac{110}{3}\dfrac{m}{s}\] into \[\dfrac{km}{hr}\] by multiplying it with \[\dfrac{18}{5}\] . So, we will get as
\[\dfrac{110}{3}\times \dfrac{18}{5}=\dfrac{110\times 6}{5}=132\dfrac{km}{hr}\]
Now, we know that speed of \[\text{train1+train2=relative speed}\] . So, on substituting the values we will get as
\[\text{50+train2=132}\]
On solving this, we get speed of train2 as
\[\text{train2}=132-50=82\dfrac{km}{hr}\]
Thus, the speed of the second train is \[82\dfrac{km}{hr}\] .
Option (d) is the correct answer.

Note: Another approach of solving this problem is by assuming speed of the second train as x. So, relative speed will be \[\left( 50+x \right)\dfrac{km}{hr}\] . Now, we will convert this into \[\dfrac{m}{s}\] by multiplying it with \[\dfrac{5}{18}\] so, we will get relative speed as \[\left( \dfrac{250+5x}{18} \right)\dfrac{m}{s}\] . Then we will use the formula \[\text{Relative speed=}\dfrac{\text{total distance}}{\text{time taken}}\] . On substituting all the values, we will get as
\[\left( \dfrac{250+5x}{18} \right)\dfrac{m}{s}=\dfrac{220}{6}\dfrac{m}{s}\]
In solving this, we will get an answer as \[x=82\dfrac{km}{hr}\].