SOLUTION: This is from one of my son's homework assignments already turned in, but I am out of practice on word problems and the correct answer to this one escaped me

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Question 97896: This is from one of my son's homework assignments already turned in, but I am out of practice on word problems and the correct answer to this one escaped me -
2 swimmers start out from the opposite ends of a pool, R and B. They cross each other for the first time at at a point 32 yards from R. They both reach the opposite end from where they started, turn around and and cross again at a point 18 yards from B. They are both traveling at a constant speed (unknown for each), what is the total length of the pool?
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
2 swimmers start out from the opposite ends of a pool, R and B. They cross each other for the first time at at a point 32 yards from R. They both reach the opposite end from where they started, turn around and and cross again at a point 18 yards from B. They are both traveling at a constant speed (unknown for each), what is the total length of the pool?
;
Let x = length of the pool (RB)
:
Draw a rough diagram and try to visualize what's going on:
R---------->32------------18<--------B
:
Distance traveled to the 1st meeting
Swimmer R = 32 yds
Swimmer B = (x-32) yds
:
Distance traveled from the 1st meeting to the 2nd meeting
R = (x-32) + 18
R = x - 14
:
B = 32 + (x-18)
B = x + 14
:
The ratio of R dist to B dist will remain the same so we have:
=
:
Cross multiply:
(x-14)(x-32) = 32(x+14)
:
x^2 - 46x + 448 = 32x + 448
:
x^2 - 46x - 32x + 448 - 448 = 0
:
x^2 - 78x = 0
:
x(x-78) = 0
;
x = +78 yds is the length of the pool
:
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SOLUTION: This is from one of my son's homework assignments already turned in, but I am out of practice on word problems and the correct answer to this one escaped me - 2 swimmers start o