Question

A man in a train notices that he can count $21$ telephone posts in one minute. If they are known to be $50$ meters apart, then at what speed is the train travelling?
A) $57\;{\rm{km/hr}}$
B) $60\;{\rm{km/hr}}$
C) $63\;{\rm{km/hr}}$
D) $55\;{\rm{km/hr}}$

Answer 1

Hint: In the solution, first we have to find the total distance of the 21 posts. Since the time is given and the total distance is calculated, we have to find the speed of the train. For that we need to use the speed formula of the train. Speed of an object is obtained using the formula, ${\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}}$.

Complete step by step answer:
Given, the distance between two telephone posts is $50\;{\rm{m}}$.
Since, there are 21 equally spaced telephone posts, so calculating the total distance of the telephone post.
Therefore, the distance from the first to the ${\rm{2}}{{\rm{1}}^{{\rm{th}}}}$ telephone post
$\begin{array}{l} = 20 \times 50\;{\rm{m}}\\ = {\rm{1000}}\;{\rm{m}}\end{array}$
Now, time taken to cross these posts
$\begin{array}{l} = {\rm{1}}\;{\rm{minute}}\\ = 60\;\sec \end{array}$
It is known that the formula to determine speed is $s = \dfrac{d}{t}$, where $s$ is speed, $d$ is distance, and $t$ is time taken.
Now, speed of the train,
$\begin{array}{c}s = \dfrac{d}{t}\\ = \dfrac{{1000\;{\rm{m}}}}{{60\;\sec }}\end{array}$
Now, convert it to ${\rm{km/hr}}$.
We know that ${\rm{1}}\;{\rm{m}} = \dfrac{1}{{1000}}\;{\rm{km}}$ and ${\rm{1}}\;{\rm{sec}} = \dfrac{1}{{60 \times 60}}\;{\rm{hr}}$
Therefore, the speed of the train is
$\begin{array}{c}\dfrac{{{\rm{1000}}\;{\rm{m}}}}{{60\;\sec }} = \dfrac{{1000 \times \dfrac{1}{{1000}}}}{{60 \times \dfrac{1}{{60 \times 60}}}}\\
= \dfrac{1}{{\dfrac{1}{{60}}}}\\
= 60\;{\rm{km/hr}}\end{array}$
Thus, the train's required speed is $60\;{\rm{km/hr}}$.

Hence the correct option is B.

Note: Speed is a scalar number, referring to "how fast an object goes." Speed can be defined as the pace at which an object covers distance. A fast-moving object has a high velocity and can travel a fairly wide distance in a short time. Speed of an object is obtained using the formula, ${\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}}$. Here we have to determine the speed of the train for the given information. Since the total distance covered and the time taken by the train can be calculated. By substituting the calculated distance and the time in the formula we can calculate the required speed of the train.