Question

A man covers a distance of 15Km in 3 hours partly by walking or partly by running. If he walks at 3 km/hr. and runs at 9 km/hr. find the distance he covers by running.

Answer 1

Hint: In this particular question assume any variable “t” in hours be the time he takes while walking so the time he takes in running is (3 - t) as the total time he takes is 3 hours. Now the sum of the multiplication of respective times and respective speeds is equal to the total distance he covered, so use these concepts to reach the solution of the question.

Complete step by step answer:
Given data:
Total distance (D) a man covered = 15 Km.
And he takes 3 hours to cover this distance.
Now it is given that he walks at 3 km/hr. and runs at 9 km/hr.
Let the time taken by him during walking be ${t_1}$ hours, so the time taken by him during running is $\left( {3 - {t_1}} \right)$ hours, as the total time is 3 hours.
Now the total distance covered by him is 15 Km, so the sum of the multiplication of respective times and respective speeds is equal to the total distance he covered.
$ \Rightarrow 3\left( {{t_1}} \right) + 9\left( {3 - {t_1}} \right) = 15$
Now simplify this we have,
$ \Rightarrow 3{t_1} + 27 - 9{t_1} = 15$
$ \Rightarrow 6{t_1} = 12$
$ \Rightarrow {t_1} = 2$ Hours.
So the time taken by him during running = (3 – 2) = 1 hour.
So the distance covered by him during running is the product of his speed during running and the time taken by him during running.
So the distance covered by him during = 9 (1) = 9 Km.

So, 9 is the required answer.

Note: Whenever we face such types of questions the key concept we have to remember is that the distance covered by him during running is the product of his speed during running and the time taken by him during running, so first calculate the time taken by him during running as above, then substitute this value in the above described formula and simplify we will get the required distance covered by him during.