Question

A man completes a journey in 10 hours. He travels the first half of the journey at the rate of 21 km/hr and the second half at the rate of 24 km/hr. Find the total journey in km.
(a) 220 km
(b) 224 km
(c) 230 km
(d) 234 km

Answer 1

Hint: Let us assume that the total distance of the journey is x. Now, find the time taken to cover half of the journey with a speed of 21 km/hr and also the time taken to cover the other half of the journey with a speed of 24 km/hr. The time is being calculated using the formula between speed, distance and time $Speed={\displaystyle \frac{\text{Distance}}{\text{Time}}}$. Now, add the time that we have got in each half of the journey and equate them to 10. Hence, we will find the value of x.

Complete step by step answer:
Let us assume that the total distance a man travelled in a journey is x km.
Now, it is given that the man travelled half of the distance i.e. ${\displaystyle \frac{x}{2}}$ with a speed of 21 km/hr. Then the time taken by the man to travel ${\displaystyle \frac{x}{2}}$ is going to be calculated by using the following formula:
$Speed={\displaystyle \frac{\text{Distance}}{\text{Time}}}$
Substituting distance as ${\displaystyle \frac{x}{2}}$ and speed as 21 in the above formula we get,
$\begin{array}{rl}& 21={\displaystyle \frac{{\displaystyle \frac{x}{2}}}{\text{Time}}}\\ & \Rightarrow Time={\displaystyle \frac{x}{2\left(21\right)}}={\displaystyle \frac{x}{42}}\end{array}$
This is the time that a man took in travelling the first half of the journey.
Now, we are going to calculate the time taken by a man to travel the other half of the journey with a speed of 24 km/hr.
$Speed={\displaystyle \frac{\text{Distance}}{\text{Time}}}$
Substituting distance as ${\displaystyle \frac{x}{2}}$ and speed as 24 in the above formula we get,
$\begin{array}{rl}& 24={\displaystyle \frac{{\displaystyle \frac{x}{2}}}{\text{Time}}}\\ & \Rightarrow Time={\displaystyle \frac{x}{2\left(24\right)}}={\displaystyle \frac{x}{48}}\end{array}$
It is given that the total time taken by a man to cover the total journey is 10 hours so adding the time of the two halves of the journey and adding them to 10.
$\begin{array}{rl}& {\displaystyle \frac{x}{42}}+{\displaystyle \frac{x}{48}}=10\\ & \Rightarrow x\left({\displaystyle \frac{8+7}{336}}\right)=10\\ & \Rightarrow x\left({\displaystyle \frac{15}{336}}\right)=10\\ & \Rightarrow x={\displaystyle \frac{10\times 336}{15}}=224\end{array}$
Hence, the distance of the journey is equal to 224 km.

So, the correct answer is “Option B”.

Note: In the above problem, the possibility of making calculation mistakes is pretty high. The other thing to keep in mind is that the units of speed, distance and time are in sync with each other.
For instance in the below formula,
$Speed={\displaystyle \frac{\text{Distance}}{\text{Time}}}$
If speed is in km/hr, then units of distance should be in km and time should be in hour.
Luckily in this problem, time, distance and speed are already given in such a way that they are in sync with the above formula. But in other questions, you won’t be that lucky and might be time is given in minutes and speed is in km/hr and distance is in km then you have to convert time in hr to make the speed, distance and time sync with each other.