Question : A man starts running from point P at 11:00 am with a speed of 10 km/h. 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 pm from point P and runs nonstop at a speed of 15 km/h towards the first man. At what time (pm) will the first man be caught?
Option 1: 6:20
Option 2: 4:40
Option 3: 6:00
Option 4: 5:30
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Correct Answer: 4:40
Solution :
Given: The man starts running at 11 am with a speed = 10 km/h
According to the question,
Distance covered by him till 2:00 PM, including one hour rest = 10 × 2 = 20 km
Now, the distance covered by him till 5:00 PM, including one-hour rest = 10 × 2 = 20 km
Total distance covered by him = 20 + 20 = 40 km
Thus, the time taken by another man to cover 40 km with a speed of 15 km/h is:
Time = $\frac{\text{Distance}}{\text{Speed}}$ = $\frac{40}{15}$ = $2\frac{2}{3}$ = 2 hours 40 minutes.
So, another man catches the first man = 2:00 + 2:40 = 4:40 PM
Hence, the correct answer is 4:40 PM.
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