Question

A person wants to travel a distance of 50km by his bicycle he travels with a speed of $12.5km/hr$. After every, $12.5km$ he takes a rest of $20{\text{minutes}}$ . How much time will he take to complete the whole distance?

Answer 1

Hint: In this type of question with the help of speed, distance, and time relation, we will find the time taken by the person to travel $50km$ at a speed of $12.5km/hr$ and addition of time of $20{\text{minutes}}$ for every $12.5km$.

Formula used:
Time, $T = \dfrac{D}{S}$
Here, $T$ , will be the time
$D$, will be the distance
$S$, will be the speed

Complete step by step solution:
In this question, it is given that,
The distance a person wants to travel will be $50km$
The speed at which he travels $50km$ on a bicycle will be $12.5km/hr$
Time consumed on taking rest at each $12.5km$ will be $20{\text{minutes}}$ .
So, by using the speed, distance, and time relation which is $T = \dfrac{D}{S}$
Therefore, the time is taken by the person to cover a distance $50km$ at a speed of $12.5km/hr$ is
$ \Rightarrow T = \dfrac{{50}}{{12.5}}$
And on solving the above time, we get
$ \Rightarrow T = 4hours$, and we will name it equation $1$
Since the time consumed on taking rest at every $12.5km$ is $20{\text{minutes}}$
So by using the unitary method,
Therefore, $50km$ the time consumed will be given by
\[ \Rightarrow 20 \times 4{\text{ minutes}}\]
And on solving, we get
$ \Rightarrow 80{\text{ minutes}}$
And in an hour it can be written as $1hour{\text{ 20 minutes}}$
So, the time taken by the person on a bicycle to cover a distance of $50km$ at a speed of $12.5km/hr$ and taking a rest of $20{\text{minutes}}$ at every $12.5km$ is
$ \Rightarrow 4hours + 1hour{\text{ 20 minute}}$
And on adding, we get
$ \Rightarrow 5 hours{\text{ 20 minute}}$

Therefore, the time taken will be $5 hours{\text{ 20 minute}}$.

Note:
Questions regarding speed, time, and distance get complicated when the units are changed so we should always convert the units into SI units first, and then we should proceed with the solution. While solving we should try to use the unitary method as it makes the problem easy to solve.