In a 800 m race around a stadium having the circumference of 200 m, the top runner meets the last runner on the 5th minute of the race. If the top runner runs at twice the speed of the last runner, what is the time taken by the top runner to finish the race ?
Answers
Answer:
Step-by-step explanation:
Let A be the top runner and B be the last runner
Both A and B starts running at same time..
After 5 mins A and B meet..A completes 400m and B completes 200m (Ratio of speed is 2:1)
After another 5 mins A completes 800m and B completes 400m.. Thereby A finishes the race..
Time taken by A = 5+5=10mins
The time taken by the fastest runner to finish the race is 10 min
Given: Total distance of race = 800 m
Circumference of circular stadium = 200 m
The top runner meets the last runner on the 5th minute of the race.
The top runner runs at twice the speed of the last runner
To Find: The time taken by the top runner to finish the race
Solution:
- As the top runner runs at twice the speed of the last runner, the distance covered by the top runner will also be twice the distance covered by the last runner.
- Accordingly, while the last runner completes one round, the top runner completes two rounds in 5 min, and they meet each other at this point.
Now, distance covered by top runner as he completes two rounds is,
= 2 × 200 m
= 400 m
So, now applying the formula for calculating the speed of the faster runner,
distance = speed × time
⇒ 400 = speed × 5
⇒ speed = 80 m/min
Now for calculating total time, the total distance = 800 m [given]
∴ Total time required by the faster runner = distance / speed
= 800 / 80
= 10 min
Hence, the time taken by the fastest runner to finish the race is 10 min
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