Question

A train is travelling at a rate of $ 45\;km/hr $ . How many seconds it will take to cover a distance of $ \dfrac{4}{5}\;km $ :
A. $ 36\;\sec $
B. $ 64\;\sec $
C. $ 90\;\sec $
D. $ 120\;\sec $

Answer 1

Hint: Firstly check the time taken by the train to cover one kilometer and then find the time taken to cover distance of $ \dfrac{4}{5}\;km $ and then convert the time taken to seconds. This method is also called a unitary method.

Complete step-by-step answer:
A train is travelling at a rate of $ 45\;km/hr $ .
As given in the question, the speed of the train is equal to $ 45\;km/hr $ . In simpler words we can also say that the train takes $ 1 $ hour to complete $ 45 $ kilometers of distance.
The train will take $ \dfrac{1}{{45}} $ hour to complete $ 1 $ kilometer of distance in the same instance.
Then the train will cover the distance of $ \dfrac{4}{5}\;km $ in $ \dfrac{1}{{45}} \times \dfrac{4}{5} = \dfrac{4}{{225}}\;hr $ .
So, the time taken in hours to cover the distance of $ \dfrac{4}{5}\;km $ is equal to
$ \dfrac{4}{{225}}\;hr $ .
There are always $ 60 $ minutes in each hour and $ 60 $ seconds in each minute. So in an hour there are always $ 3600 $ seconds.
Now convert the time taken to cover the distance of $ \dfrac{4}{5}\;km $ in seconds:
 $
  \dfrac{4}{{225}}\;hr = \dfrac{4}{{225}} \times 3600\;\sec \\
   = 64\;\sec \;
  $ .
So, the time taken to cover a distance of $ \dfrac{4}{5}\;km $ in seconds is equal to $ 64\;\sec $ .
So, the correct answer is “Option B”.

Note: The speed of the train is given in kilometer per hour units and the time for travelling $ \dfrac{4}{5}\;km $ is asked in seconds. So, the units must be converted to get the right answer in the right unit.