Question

A man is walking at a speed of 15 km per hour. After every kilometer, he takes a rest for 3 minutes. How much time will he take to cover a distance of 4 km?
a. 25 min
b. 30 min
c. 20 min
d. 35 min

Answer 1

Hint: We will use the unitary method to find the time taken by the man to cover a distance of 1km. We will then add 3 minutes after every 1km distance covered. We will repeat this till 3km is covered. In the last step when it's 4km, we will not add 3 minutes extra as the target is already achieved.

Complete step by step solution:
It is given in the question that a man is walking at a speed of 15 km per hour. After every kilometer, he takes a rest for 3 minutes. And we have been asked to find how much time he will take to cover a distance of 4 km.
We will use the unitary method to find the time taken by the man to cover a distance of 1km. So, for that we need to have an idea about the unitary method. So, unitary method is a method in which we find the value of 1 unit first, and then we multiply it with the required number to get the desired value.
Now, from the question we get that the speed of the man is 15 km/h. It means that the man can travel 15 km in 1 hour, that is, 60 minutes. So, the time taken by the man to travel 1km will be,
$\dfrac{60}{15}=4\min $
So, the time taken by the man to cover 1km is 4 minutes.
It is given that he rests after every 1km for 3 minutes. So, the actual time taken to cover 1km including the rest time after 1km will be (4 min + 3min) = 7 min.
Similarly, the time taken to complete the second km including the rest time will be (4min + 3min) = 7min.
And the time taken to cover the third km including the rest time will be, (4min + 3min) = 7min.
The time taken to cover the fourth km will be 4 minutes only, as our question is to find the distance covered by the man in 4km, so we don’t have to add the time taken to rest after 4km.
Therefore, the total time taken by the man to cover 4km will be 7 + 7 + 7 + 4 = 25 minutes.
Thus, the man will take 25 minutes to cover a distance of 4km if he walks at a speed of 15 km per hour and after every kilometer, he takes rest for 3 minutes.
Hence, option (a) is the correct answer.

Note: The most common mistake that the students make while solving this question is that they may add the rest time, that is, 3 minutes after covering 4km, and as a result they may get the answer as 28 minutes, which is wrong. This error can also occur, as the students think that the time taken by the man to cover every 1km is 7 minutes, so they directly multiply, $7\times 4$, and get 28 minutes as their answer. So, the students must solve this question step by step in order to avoid any mistakes.