Question 473398: 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 if they began at the same time?
Found 2 solutions by ankor@dixie-net.com, ccs2011:
Answer by ankor@dixie-net.com(22740)   (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 began at the same time?
:
Let t = time required for the faster runner to overtake the slower
:
Write a distance equation: dist = speed * time
:
10t = 6t + 70
10t - 6t = 70
4t = 70
t = 
t = 17.5 seconds
:
:
Check this, the faster runner has to cover 70 m more than the slower
1.75*10 = 175 m
17.5*6 = 105 m
Answer by ccs2011(207)  (Show Source):
You can put this solution on YOUR website! Distance = rate*time
d= r*t
Goal is to find time it takes for faster runner to catch up with slower runner. At this time the faster runner will have traveled 70 more meters than slower runner.
Let d1 be faster runner and d2 be slower runner.
d1 = d2 + 70
d1 = 10t
d2 = 6t
Substitute these into 1st equation and solve for t:
10t = 6t + 70
Subtract 10t on both sides
4t = 70
Divide by 4 on both sides
t = 17.5
Therefore, it will take 17.5 seconds for faster runner to catch up
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