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Question 818401: Pat and Jane want to paint a fence, pat can paint the fence by himself in 3 hours, jane can paint the fence by herself in 4 hours. At noon, they start painting the fence together. At some point, they argue for ten minutes, and no painting gets done. After the arguement, jane leaves and pat paints alone. If pat finishes painting at 2:25 pm, at what time did the argument begin? How do u solve.....is it a work rate problem?
Found 2 solutions by richwmiller, josmiceli:
Answer by richwmiller(17219)   (Show Source):
You can put this solution on YOUR website! It is a rate of work problem that you need to break down into several parts. My favorite!
normally
x/3+x/4=1
4x/12+3x/12=1
7x/12=1
x=12/7 working together
This is what we expect with BUT IT IS NOT the question.
We have three times we need to use
t for time together
a for time arguing
p for pat's time alone
t+a+p=2+25/60,
a=10/60,
t/3+t/4+ p/4=1
we have three unknowns and three equations
It can be solved
a = 1/6, p = 15/16, t = 21/16 in hours
a=0.16667, p=0.93750, t=1.3125 in hours
a = 10, p = 225/4, t = 315/4 in minutes
a=10, p=56.250, t=78.750 in minutes
They worked 21/16 hours or 78.75 minutes together
they argued at 1:18:45 pm
They argued for 10 minutes
Pat worked 15/16 of an hour alone
we could have converted everything to minutes to begin with
t+a+p=145,
a=10,
t/180+t/240+ p/240=1
t+a+p=145, a=10, t/180+t/240+ p/240=1
we get the same answers
a = 10, p = 225/4, t = 315/4 in minutes
a=10, p=56.250, t=78.750 in minutes
Answer by josmiceli(19441)  (Show Source):
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