Question 473179: Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 6 meters per second. If the slower runner has a 70-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
Found 2 solutions by amoresroy, Alan3354:
Answer by amoresroy(361)   (Show Source):
You can put this solution on YOUR website! Two persons are to run a race, but one can run 10 meters per second, whereas the other can run 6 meters per second. If the slower runner has a 70-meter head start, how long will it be before the faster runner catches the slower runner, if they begin at the same time?
Let x = the number of seconds it will take the faster runner to catch up with the slower runner
Take note that for the faster runner to catch up with the slower runner, his total distance should be equal to 70 meters plus distance traveled by the slower runner.
From the formula of distance (distance = speed times time),the equation should be:
10 x = 70 + 6x
10x-6x = 70
x = 70/4
x = 17.5
It will take 17.5 seconds for the faster runner to catch up with the slower runner.
Answer by Alan3354(69443)  (Show Source):
You can put this solution on YOUR website! The faster gains on the slower runner at 4 m/sec (10 - 6)
(Or, the speed of the faster runner relative to the slower is 4 m/sec)
70 m/4 m/sec = 17.5 seconds
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