Question

Two trains 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions on parallel tracks. What is the time (in seconds) which they take to cross each other?
A. 10.8 seconds
B. 11.2 seconds
C. 9.6 seconds
D. 10.4 seconds

Answer 1

Hint: Here in this question we will proceed by finding out the relative speed and the total distance covered by trains in crossing each other. Then we will use the formula of speed and time to find the time taken by the trains in crossing each other.

Complete Step-by-Step solution:
Relative speed while both cross each other = 60+40 = 100km/hr
$\begin{gathered}
   = 100 \times \dfrac{5}{{18}}m/\sec \\
   = \dfrac{{250}}{9}m/\sec \\
\end{gathered} $ ( converting km/hr into m/sec by multiplying it with $\dfrac{5}{{18}}$ )
Now we know that the distance covered in crossing each other is the sum of the lengths of both trains .
$ \Rightarrow {\text{distance = 140 + 160 = 300 m}}$
Hence ${\text{time = }}\dfrac{{{\text{distance}}}}{{{\text{speed}}}}$
$ \Rightarrow time = \dfrac{{300}}{{\dfrac{{250}}{9}}} = \dfrac{{300 \times 9}}{{250}} = \dfrac{{54}}{5} = 10.8\sec $ .
Therefore they would take 10.8 seconds to cross each other.
Option A is Correct.

Note: In this particular type of question the basics about speed and distance calculation should be recalled. Always remember to change two different quantities before calculating them together. Here we multiplied by $\dfrac{5}{{18}}$ which was the simplest form of conversion of km/hr to m/s. It is just the fractional form of the total number of meters in a km and number of seconds in an hour.