Question 1177797: Eddie and Missy are swimming laps in parallel lanes of a swimming pool
at different constant speeds. They start simultaneously at opposite ends of the pool. They first pass each other when Eddie has swum 72 feet. Both turn back when they reach the opposite ends, and they next pass each other when Eddie is 40 feet from Missy’s starting point. What is the length of a lap?
Answer by ikleyn(52803)   (Show Source):
You can put this solution on YOUR website! .
Eddie and Missy are swimming laps in parallel lanes of a swimming pool at different constant speeds.
They start simultaneously at opposite ends of the pool. They first pass each other when Eddie has swum 72 feet.
Both turn back when they reach the opposite ends, and they next pass each other when Eddie is 40 feet
from Missy’s starting point. What is the length of a lap?
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Let d be the unknown length of the swimming pool (same as the swimming lap).
To get first meeting point, Eddie covered 72 feet; Missy covered (d-72) feet.
They spent the same time to get the meeting point, so the ratio of their speeds was  (Eddie to Missy).
Starting from their first meeting point to the second meeting point,
Eddie covered (d-72)+40 feet = d-32 feet; Missy covered 72 + (d-40) = d+32 feet.
Again, from the first meeting point to the second meeting point, they spent the same time, so, the ratio
of their speeds was  (Eddie to Missy).
This ratio is the same in both cases, which gives you THIS equation
= .
From the equation, cross-multiplying, you get
(d-72)*(d-32) = 72*(d+32)
d^2 - 104d + 72*32 = 72d + 72*32
d^2 - 176d = 0
d*(d-176) = 0.
Obviously, the solution is the positive root of this equation d= 176 feet.
ANSWER. The lap length is 176 feet.
Solved.
Nice Travel & Distance problem . . .
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