SOLUTION: 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.

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): You can put this solution on YOUR website!
it's a work problem that is divided
into 3 parts:
(1) painting done by both
(2) short period of no painting
(3) painting done by Pat alone
------------------------
Let = the amount of time in hours
from noon to when they started their
10 minute argument
-----------------
Let = the amount of time in hours
from the end of the 10 minute argument
to 2:25 PM
---------
Let = the fraction of the job that they
both get done in the 1st time period
----------------------------
= the fraction of the job that
Pat does in the 3rd time period
-------------------------
-------------------------
For the 1st time period, I can say:

Multiply both sides by

(a)
----------------
Fot the 3rd time period:

Multiply both sides by

(b)
-----------------
So far I have 2 equations and 3 unknowns.
The 3rd equation is:

( note that I converted minutes to hours )

(c)
Substitute (a) and (b) into (c)
(c)
Multiply both sides by
(c)
(c)
(c)
(c)
---------------
(a)
(a)
(a)
(a)
and
(b)
(b)
(b)
(b)
(b)
------------------
check:

OK
-------
Noon plus =

The argument began at 1:18:45
Unless I made a mistake- check the work

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