Question

A car travelling at a speed of 60 km/hr takes 15 hours to complete a journey. What will be the time taken to complete the same journey by a train whose speed is 90 km/hr?

Answer 1

Hint: Let us assume that the distance of the journey is “x km''. We have given the speed and time to complete the journey from this information, we can find the distance using the formula of speed, distance and time which is given as $\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$. After substituting the value of speed as 60 km/hr and time as 15 hours we will get the distance of journey. Now, using this distance of the journey and speed as 90 km/hr in the formula $\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$ we will get the time required to complete the same journey with speed 90 km/hr.

Complete step-by-step answer:
It is given that the speed of the car is 60 km/hr and time taken to complete the journey is 15 hours. Let us assume that the distance of the journey is “x km”. Now, to find this distance we are going to use the formula which is the relationship between speed, distance and time.
$\text{Speed}=\dfrac{\text{Distance}}{\text{Time}}$………. Eq. (1)
Substituting the speed as 60 km/hr, time as 15 hours and distance of the journey as “x km” in the above equation we get,
$60km/hr=\dfrac{\text{x }}{\text{15 hours}}$
On cross multiplying the above equation we get the value of x as:
\[\begin{align}
  & \left( 60\times 15 \right)km=x \\
 & \Rightarrow 900km=x \\
\end{align}\]
Now, we have got the distance of the journey as 900 km.
We are asked to find the time taken to complete the distance of 900 km with a speed of 90 km/hr. Let us assume that time taken is “t hours”. Substituting these values of distance, time and speed in eq. (1) we get,
$90km/hr=\dfrac{900km}{t}$
On cross multiplying the above equation we get,
$90t=900$
Dividing 90 on both the sides of the above equation we get,
$\begin{align}
  & t=\dfrac{900}{90} \\
 & \Rightarrow t=\text{10 hours} \\
\end{align}$
Hence, 10 hours will be taken to complete the same journey when the car is going with a speed of 90 km/hr.

Note: In this problem you are lucky that units of speed, distance and time are syncing with each other. For e.g., in some questions you have given speed in m/s whereas distance is given in km and time is given in hours then you have to first convert speed in km/hr then substitute these values in the formula of speed, distance and time. You can avoid making such mistake by substituting the values of speed, distance and time in the formula with units like the example that we have shown above if you put values with units then you will find that:
$\begin{align}
  & \text{Speed}=\dfrac{\text{Distance}}{\text{Time}} \\
 & \Rightarrow m/s=\dfrac{\text{km}}{\text{hour}} \\
\end{align}$
As you can see that L.H.S is not equal to R.H.S so we have to convert either m/s into km/hr given on the L.H.S or convert km in m and hours into seconds given on the R.H.S of the above equation.