SOLUTION: It takes Ralph 8 hours to paint a fence alone. Lisa can do the same job in 11 hours. If Ralph paints alone for 35 minutes before Lisa begins helping, how long must they work toget

Algebra ->  Rate-of-work-word-problems -> SOLUTION: It takes Ralph 8 hours to paint a fence alone. Lisa can do the same job in 11 hours. If Ralph paints alone for 35 minutes before Lisa begins helping, how long must they work toget      Log On


   

Question 950277: It takes Ralph 8 hours to paint a fence alone. Lisa can do the same job in 11 hours. If Ralph paints alone for 35 minutes before Lisa begins helping, how long must they work together to finish painting the fence? Give your answer as a simplified fraction.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Ralph's rate of painting is:
( 1 fence ) / ( 8 hrs )
+35+ min = +35%2F60+=+7%2F12+ hrs
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In +35+ min, Ralph paints:
+%28+1%2F8+%29%2A+%28+7%2F12+%29+=+7%2F96+ fraction of the fence
That means there is +1+-+7%2F96+=+89%2F96+
of the fence left to paint
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Add their rates of painting to get rate painting together
Let +t+ = time in hrs for them to paint
the fence working together
+1%2F8+%2B+1%2F11+=+%28%28+89%2F96+%29%29+%2F+t+
Multiply both sides by +11%2A96t+
+11%2A12t+%2B+96t+=+11%2A89+
+132t+%2B+96t+=+979+
+228t+=+979+
+t+=+979%2F228+ hrs
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Doesn't seem right if they mention "simplified"
I think my method is right, though -check the
math & get another opinion, too