SOLUTION: 1)Two swimmers start out from opposite sides of a pool, Each swims the length of the pool and back at constant rate. they pass each other for the first time 40 feet from one side o

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Question 934510: 1)Two swimmers start out from opposite sides of a pool, Each swims the length of the pool and back at constant rate. they pass each other for the first time 40 feet from one side of the pool and second time 45 feet from the other side of the pool. what is the length of the pool?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Two swimmers start out from opposite sides of a pool,
Each swims the length of the pool and back at constant rate.
they pass each other for the first time 40 feet from one side of the pool and
second time 45 feet from the other side of the pool.
what is the length of the pool?
:
let x = the length of the pool
then at the 1st meeting
1st swimmer swam 40 ft
2nd swimmer swam (x-40) ft
:
At the 2nd meeting:
1st swimmer swam (x-40) + 45 = (x+5) ft
2nd swimmer swam 40 + (x-45) = (x-5) ft
:
The ratio of the distances the two swimmers is the same for each meeting, therefore
40%2F%28%28x-40%29%29 = %28%28x%2B5%29%29%2F%28%28x-5%29%29
cross multiply
40(x-5) = (x-40)(x+5)
40x - 200 = x^2 + 5x - 40x - 200
combine like terms
0 = x^2 - 35x - 40x - 200 + 200
0 = x^2 - 75x
factor out x
x(x - 75) = 0
x = 0
and
x = 75 ft is the length of the pool (a standard 25 yd pool)
;
;
see if that checks out,
1st swimmer swam 40 ft to the 1st meeting, and 80 ft to the second meeting
2nd swimmer swam 35 ft to the 1st meeting and 70 ft to the second meeting