SOLUTION: Jake gave Patti a 5-yard head start in a 100-yard dash and Jake lost by only 1/4 yard. In how many more yards, beyond 100 yards, would Jake have overtaken Patti?

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Question 254824: Jake gave Patti a 5-yard head start in a 100-yard dash and Jake lost by only 1/4
yard. In how many more yards, beyond 100 yards, would Jake have overtaken
Patti?

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Jake gave Patti a 5-yard head start in a 100-yard dash and Jake lost by only 1/4
yard.
In how many more yards, beyond 100 yards, would Jake have overtaken
Patti?
:
When P's at the 100 yd marker, P has ran 95 yds in the same time interval as J ran 99.75 yds
Use this to establish the speed of each runner
:
Let d = distance beyond the 100 yd marker where J overtakes P
:
Write a time equation Time = dist/speed
d%2F95 = %28d%2B.25%29%2F99.75
cross multiply
99.75d = 95(d+.25)
:
99.75d = 95d + 23.75
:
99.75d - 95d = 23.75
:
4.75d = 23.75
d = 23.75%2F4.75
d = 5 yds past the 100 yd maker, J catches P
:
:
Confirm this by finding the times
5/95 = .0526
5.25/99.75 = .0526; J ran 51%2F4 yds in the same time P ran 5 yds