SOLUTION: Two athletes race around a 400-m track oval at a speed of 6 and 8 meters per second, respectively. How long will it take before the faster athlete gains one lap on the slower one?

Question 354067: Two athletes race around a 400-m track oval at a speed of 6 and 8 meters per second, respectively. How long will it take before the faster athlete gains one lap on the slower one?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
speed of one athelete = 6 m/sec
speed of second = 8 m.sec
Since they are running in the same direction the effective speed = 8-6 = 2 m/s.
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It means runner 2 will catch up 2 meters every second.
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if he has to catch up 1 lap which is 400m he will take 400/2 = 200 seconds.

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There is another method of solution

Let runner 1 run x m when runner 2 is 400m ahead
distance run by runner 2 will be x+400
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speed of runner 1 = 6m/s
speed of runner 2 = 8m/s
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The time taken is the same
time = distance/speed.
x/6 = (x+400)/8
8x=6(x+400)
8x=6x+2400
8x-6x = 2400
x= 1200 m the distance run by runner 1 when runner 2 gains 1 lap.
speed of runner 1 = 6 m/s
time taken = 1200/6 = 200 seconds
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distance run by runner 2 = 1200+400 = 1600 m
speed = 8m/s
time taken = 1600/8 = 200seconds
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The seond method is algebraic. the first is arithmetic.

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