Question

It takes $ 2\;{\rm{hrs}} $ for a train to cover a distance of $ 150\;{\rm{km}} $ . How much time will it take to cover a distance of $ 450\;{\rm{km}} $ if it travels with the same speed?
A. $ 4 $
B. $ 6 $
C. $ 15 $
D. $ 3 $

Answer 1

Hint: The number of hours is directly proportional to distance travelled. So the ratio between the first number of hours and distance travelled is equal to the ratio between the second number of hours and distance travelled. Then we will get the time travelled by the train for the distance of $ 450\;{\rm{km}} $ .

Complete step-by-step answer:
Given the number of hours took by the train to cover the distance of $ 150\;{\rm{km}} $ is $ 2{\rm{ hrs}} $ .
Given the $ 2{\rm{ hrs}} $ covered distance is $ 150\;{\rm{km}} $ .
Given the $ n{\rm{ hrs}} $ covered distance is $ 450\;{\rm{km}} $ .
So, the main aim in our problem is to find the number of hours took by the train to cover the distance of $ 450{\rm{ km}} $ .
We know one property that time is always proportional to distance travelled. So, the train is moving with the same speed that is the formula for to find the speed is,
 $ {\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}} $
On substituting the distance and time values in the above equation we get,
 $ \begin{array}{l}
{\rm{speed}} = \dfrac{{150}}{2}\\
{\rm{speed}} = 75{\rm{ km/h}}
\end{array} $
Since, the speed for both the distance are equal so,
 $ {\rm{speed}} = \dfrac{{{\rm{distance}}}}{{{\rm{time}}}} $
On substituting the speed and distance in the above expression, we get,
 $ 75 = \dfrac{{450}}{t} $
By rearranging and simplifying all the terms in the above equation we get,
 $ \begin{array}{c}
t = \dfrac{{450}}{{75}}\\
 = 6{\rm{ hrs}}
\end{array} $
The time taken for the train to cover the distance of $ 450\;{\rm{km}} $ is $ 6{\rm{ hrs}} $ .
So, the correct answer is “Option B”.

Note: In this problem, we can use this method only when speed will be the same. If the speed is different then, it would be difficult to find the number of hours the train reaches some distance.