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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. He continues this 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?

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. He continues this 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? Correct Answer 4 : 40

Formula used:

Distance = Speed × Time 

Calculation:

Let the first and second person be A & B.

⇒ A starts running at 11 am with a speed = 10 km/hr 

According to the question,

⇒ He runs for 2 hours and rests for 1 hour and this alternative running and resting loop repeated.

Then, Distance covered by A in the first 3 hours i.e. till 2 pm

= 10 × 2 = 20 km

Now, the distance covered by A in next 3 hours i.e. till 5 pm

= 10 × 2 = 20 km.

Hence, the time is taken by B to cover 40 km = 40/15 = 2 hours 40 minutes.

∴ At 4:40, A will be caught by B.

Mistake Points

Relative speed can be calculated only when both the objects in motion for the continuous-time period  in  either the same or opposite direction 

Here relative speed cannot be calculated because both A and B are not in relative motion for a continuous period, since A takes rest for 1 hour after every 2 hours of travel but B travels continuously 

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