Question

A journey of 540 km is completed in 7 hours 30 minutes. If two-third of the journey is completed at 80 km/hr, at what speed is the remaining journey completed?
(a) 60 km/hr
(b) 30 km/hr
(c) 20 km/hr
(d) 40 km/hr

Answer 1

Hint: We will find the distance of the two-third journey. The formula for speed is given as $\text{speed = }\dfrac{\text{distance}}{\text{time}}$. Then we will use the formula for speed to find the time taken to cover the two-third distance of the journey. We will again use the formula for speed to find the speed of the remaining journey by using the remaining distance and remaining time of the journey.

Complete step-by-step answer:
The given distance of the journey is 540 km. Two-third of the journey can be calculated as follows,
$\dfrac{2}{3}\times 540=360\text{ km}$.
Now, the speed to cover the two-third distance, which is 360 km, is given as 80 km/hr.
We know that $\text{speed = }\dfrac{\text{distance}}{\text{time}}$. Substituting the values of speed and distance of the two-third journey, we get the following,
$\begin{align}
  & 80=\dfrac{360}{\text{time}} \\
 & \Rightarrow \text{time = }\dfrac{360}{80} \\
 & \therefore \text{time = 4}\text{.5} \\
\end{align}$
This means, the time taken to cover the two-third distance is 4 hours 30 minutes.
Now, the remaining distance to be covered is $540-360=180\text{ km}$ and the remaining time to cover this distance is $\text{7 hours 30 minutes }-\text{ 4 hours 30 minutes = 3 hours}$. We will use the formula for speed to find the speed with which the remaining journey is completed. We have the following,
$\begin{align}
  & \text{speed = }\dfrac{180}{3} \\
 & \therefore \text{speed = 60 km/hr} \\
\end{align}$
Hence, the correct option is (a).

So, the correct answer is “Option A”.

Note: We can convert the time into minutes from hours and minutes if it is convenient for the calculations. It is essential that we know the concept of speed and its formula. We should be able to interpret the given information in the question accurately. We should also do the calculations explicitly. So that we can avoid making any minor errors in the calculations and obtain the correct answer.