In a 4000 metre race around a circular stadium having a circumference of 1000 metres, the fastest runner and the slower runner reach the same point at the end of the 5th minute, for the first time after the start of the race. If the fastest runner runs at twice the speed of the slowest runner, what is the time taken by the fastest runner to finish the race?
Answers
Answer:
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your answer is here !
Step-by-step explanation:
=> Let speed of slower runner = x m/min
⇒ Speed of faster runner = 2x m/min
=> Time taken to meet for the 1st time = 1000/2x-x = 5 min
⇒ x = 200 m/min
⇒ 2x = 400 m/min Time taken by the faster runner to finish the race = 4000/400 = 10 min
follow me !
The time taken by the fastest runner to finish the race is 10 min.
Given: Total distance of race = 4000 m
Circumference of circular stadium = 1000 m
the fastest runner and the slower runner reach the same point at the end of the 5th minute.
The fastest runner runs at twice the speed of the slowest runner
To Find: the time taken by the fastest runner to finish the race
Solution:
- As the fastest runner runs at twice the speed of the slower runner, the distance covered by the fastest runner will also be twice the distance covered by the slower runner.
- Accordingly, while the slower runner completes one round, the faster runner completes two rounds in 5 min, and they meet each other at this point.
Now, distance covered by faster runner as he completes two rounds is,
= 2 × 1000 m
= 2000 m
So, now applying the formula for calculating the speed of the faster runner,
distance = speed × time
⇒ 2000 = speed × 5
⇒ speed = 400 m/min
Now for calculating total time, the total distance = 4000 m [given]
∴ Total time required by the faster runner = distance / speed
= 4000 / 400
= 10 min
Hence, the time taken by the fastest runner to finish the race is 10 min
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