Understanding the Runner's Journey
The problem asks us to find the total time a man takes to cover a distance of 15 km. We are given his running speed and the condition that he rests for 30 minutes after completing every 4 km.
Calculating Running Time
First, let's determine the time the man spends actually running.
- The formula relating distance, speed, and time is: $$ \text{Time} = \frac{\text{Distance}}{\text{Speed}} $$
- Given:
- Speed = 6 km/h
- Total Distance = 15 km
- Running Time = $ \frac{15 \text{ km}}{6 \text{ km/h}} $
- Running Time = $ 2.5 $ hours
Calculating Rest Time
Next, we need to figure out the total time spent resting. The man rests for 30 minutes (which is $ 0.5 $ hours) after every 4 km.
- He runs 15 km in total. Let's see how many 4 km segments he completes:
- After the first 4 km: He rests.
- After the next 4 km (total 8 km): He rests again.
- After the next 4 km (total 12 km): He rests a third time.
- He then runs the remaining 3 km (from 12 km to 15 km). Since he has completed the total distance, he doesn't take another rest break *after* finishing.
- So, he takes rests at the 4 km, 8 km, and 12 km marks. This amounts to 3 rest periods.
- Each rest period is 30 minutes = $ 0.5 $ hours.
- Total Rest Time = Number of Rests $ \times $ Duration of Each Rest
- Total Rest Time = $ 3 \times 0.5 $ hours
- Total Rest Time = $ 1.5 $ hours
Determining Total Time
Finally, to find the total time taken, we add the running time and the rest time.
- Total Time = Running Time + Total Rest Time
- Total Time = $ 2.5 $ hours + $ 1.5 $ hours
- Total Time = $ 4.0 $ hours
Therefore, the man will take 4 hours to cover 15 km.
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Important Questions from Speed Time and Distance
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