SOLUTION: Aly can paint a room two hours less than AJ. If they will work together, they can finish the job in 12 hours. How long would it take each person to complete the same job working al

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: Aly can paint a room two hours less than AJ. If they will work together, they can finish the job in 12 hours. How long would it take each person to complete the same job working al      Log On


   

Question 891095: Aly can paint a room two hours less than AJ. If they will work together, they can finish the job in 12 hours. How long would it take each person to complete the same job working alone?
Answer by josgarithmetic(39616) About Me  (Show Source):
You can put this solution on YOUR website!
Aly and A.J., time for A.J. to do the job alone is t.

The description gives rates:
Aly, 1%2F%28t-2%29
A.J., 1%2Ft
Combined Aly & A.J., 1%2F12 working together.

The combined rate is simply the sum of their rates.
1%2F%28t-2%29%2B1%2Ft=1%2F12
LCD is 12t%28t-2%29, so multiply both sides by this expression.
12t%2B12%28t-2%29=t%28t-2%29
12t%2B12t-24=t%5E2-2t
26t-24=t%5E2
t%5E2-26t%2B24=0
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t=%2826%2B-+sqrt%2826%5E2-4%2A24%29%29%2F2
t=%2826%2B-+sqrt%28580%29%29%2F2
Using decimal approximation
highlight%28t=%2826%2B-+24.033%29%2F2%29
highlight%28t=25%29 or cross%28t=0.9835%29willNotWork
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A.J. could do the job alone in 25 hours.
(More accurately,25.02 hours.)