Question

A train \[100\text{ m}\] long takes 6 seconds to cross a man walking at 5km/h in a direction opposite to that of the train. The speed of the train is
A. 50km/h
B. 55km/h
C. 57 km/h
D. 60 km/h

Answer 1

Hint: First we assume the speed of the train to be \[x\] km/h. The formula that we use in solving this question would be the relation between speed, distance and time.
$\text{speed=}\dfrac{\text{distance}}{\text{time}}$
As the man is walking at 5km/h in a direction opposite to that of the train the relative speed of the train will be $x+5$ km/h.

Complete step by step answer:
We have given that a train \[100\text{ m}\] long takes 6 seconds to cross a man walking at 5km/h in a direction opposite to that of the train.
We have to calculate the speed of the train.
Let us assume that the speed of the train is \[x\] km/h.
When we consider the man as a point object, the distance covered by a train to cross a man will be equal to the length of the train i. e. \[100\text{ m}\].
Now, as given in the question the man is walking at 5km/h in a direction opposite to that of the train the relative speed of the train will be $x+5$ km/h.
So, when we put the values in the formula $\text{speed=}\dfrac{\text{distance}}{\text{time}}$, we get
\[~x+5\text{=}\dfrac{100}{6}\]\[~\Rightarrow x+5\text{ km/h =}\] $\dfrac{100\text{ m}}{6\text{ sec}}$
Now, as we know that the units on both sides of the equation must be the same. So, we convert the unit m/sec to km/h.
We know that $1\text{ m/sec = }\dfrac{18}{5}\text{ km/hr}$
Now, \[~\Rightarrow x+5\text{ km/h =}\dfrac{100}{6\text{ }}\times \dfrac{18}{5}\text{ km/h }\]
When we solve further, we get
$\begin{align}
  & \Rightarrow x+5=60 \\
 & \Rightarrow x=60-5 \\
 & \Rightarrow x=55\text{ km/h} \\
\end{align}$
So, the speed of the train is $55\text{ km/h}$. Option B is the correct answer.

Note: The point to note is that the units of all the quantities must be the same. If the units are different and we solve the question, we will get incorrect answers. We have the following equation \[~x+5\text{=}\dfrac{100}{6}\]. When we solve the equation without converting the units, we get
$\begin{align}
  & x+5=16.67 \\
 & x=16.67-5 \\
 & x=11.67 \\
\end{align}$
which is an incorrect answer. So, we have to keep the units the same for both sides of the equation.