Question

A 280m train moving with the average speed of 108 km/hr crosses a platform in 12 seconds. A boy crosses the same platform in 10 seconds. What is the speed of a boy in m/s?
\[
  A.{\text{ 5}}m/s \\
  B.{\text{ 8}}m/s \\
  C.{\text{ }}10m/s \\
  D.{\text{ Cannot be determined}} \\
 \]

Answer 1

Hint: In order to find the speed of the boy first we need the length of the platform. Find the length of the platform by the help of data given for the train and use that for proceeding further in finding the speed of the boy.

Complete step-by-step answer:

Given that: Length of the train $ = 280m$
Average speed of the train $ = 108km/hr$
Time taken by train to cross the platform $ = 12{\text{seconds}}$
As the length of the train is given in meters, time is given in seconds also the answer is required in m/s.
So let us convert the average speed of the train in m/s.
$\therefore $ Speed of the train $ = 108km/hr = 108 \times \dfrac{5}{{18}}m/s = 30m/s$ .
Let the length of the platform be $x$ meter.
As the train crosses the platform, the distance covered by the train in the given 12 seconds is the sum of the length of the platform and the length of the train. As the time of crossing of the platform begins when the front end of the train touches the platform and the time ends when the back end of the train leaves.
So, distance travelled by the train $ = {\text{length of platform + length of train}}$
$ \Rightarrow {\text{Distance}} = x + 280$
As we know the formula for speed is given by, ${\text{speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$
Putting the above value in the given formula.
\[
   \Rightarrow {\text{speed of the train = }}\dfrac{{{\text{distance travelled}}}}{{{\text{time taken}}}} \\
   \Rightarrow 30m/s = \dfrac{{\left( {x + 280} \right)m}}{{12s}} \\
 \]
Solving the above equation for the value of x.
\[
   \Rightarrow \left( {x + 280} \right) = 30 \times 12 \\
   \Rightarrow x + 280 = 360 \\
   \Rightarrow x = 360 - 280 \\
   \Rightarrow x = 80m \\
 \]
So the length of the platform is 80m.
Now proceeding with the case of the boy.
Since the boy moves along the platform, the distance covered by the boy is the same as the length of the platform which is 80m.
Distance covered by the boy $ = 80m$
Time taken by the boy $ = 10\sec $
So the speed of the boy is:
$
  {\text{speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}} \\
  {\text{speed = }}\dfrac{{80m}}{{10s}} = 8m/s \\
 $
Hence, the speed of the boy is 8m/s.
So, option B is the correct option.

Note: Always remember the concept behind the distance covered by the train when the train crosses a platform or when the train crosses a pole. Most of the questions in distance and time are related to this concept, which is also mentioned above. Major focus should be given on the units used in the problem and while doing calculation. Also remember the formula for conversion of speed from m/s to km/hr and vice-versa.