Question

A man starts running from point P at 11: 00 a.m. with a speed of 10 km / hr. He runs for 2 hours and then takes a 1-hour rest. H continues till he is caught by another man who starts at 2: 00 p.m. from point P and runs non – stop at a speed of 15 km / hr towards the first man. At what time (in p.m.) will the first man be caught?

Answer 1

Hint: To solve this question we will use the formula speed = distance / time. We will first apply this formula for first man and then for second man.

Complete step-by-step answer:

Now, let the man be denoted by A and the second man be denoted by B. Now, A starts running at 11: 00 a.m. and stops at 2: 00 p.m. for the first time. Now, he runs for 2 hours before coming to rest for the first time. So, distance covered = speed x time = 10 x 2 = 20 km.
 So, at 2: 00 p.m. a has covered a distance of 20 km. Now, again he starts running for 2 hours and time is 4: 00 p.m. when he comes to rest for the second time. So, again distance covered = 2 x 10 = 20 km.

So, total distance covered till 4: 00 p.m. = 40 km

Now, B has started running at 2: 00 p.m. with a speed of 15 km / hr. So, distance travelled by B in 2 hours = 2 x 15 = 30 km. So, the time is 4: 00 p.m.

So, at 4: 00 p.m. distance covered by B = 30 km.

So, the distance left at 4: 00 p.m. between A and B = 40 – 30 = 10 km.

Now, A has come to rest and B is still running. So, time taken by B to cover 10 km = $\dfrac{{10}}{{15}}{\text{ = }}\dfrac{2}{3}$ hr.

So, time taken = $\left( {\dfrac{2}{3}{\text{ }} \times {\text{ 60}}} \right)$ = 40 minutes.

So, after running for 2 hour 40 minutes, B will catch A. As, B starts at 2: 00 p.m.

So, at 4: 40 p.m. B will catch A.

Note: When we come up with such types of questions, we will apply the formula ${\text{speed = }}\dfrac{{{\text{distance}}}}{{{\text{time}}}}$ to solve the problem. By using this formula, we will find all the values which are asked in the question. You have to apply the formula carefully because most of the mistakes are done because of applying incorrect formulas. If any parameter (time, distance, speed) has another unit, you have to convert all the units to solve the question.