SOLUTION: Please help ! It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 17 hours. If Ralph paints alone for 45 minutes before Lisa begins helping, how long must

Algebra ->  Rate-of-work-word-problems -> SOLUTION: Please help ! It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 17 hours. If Ralph paints alone for 45 minutes before Lisa begins helping, how long must      Log On


   

Question 951384: Please help !
It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 17 hours. If Ralph paints alone for 45 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!
How much of the fence does Ralph paint in +45+ min ?
+45%2F60+=+3%2F4+ hrs
Ralph's rate of painting is:
( 1 fence ) / ( 14 hrs )
----------------------
( Ralph's rate ) x ( time spent painting ) = ( fraction of fence painted )
+%28+1%2F14+%29%2A%28+3%2F4+%29+=+3%2F56+
That means there is +1+-+3%2F56+=+53%2F56+ of the fence left to paint
----------------------
Add their rates of working to get rate working together
L:et +t+ = their time in hrs to paint the remaining
+53%2F56+ of the fence
----------------------
+1%2F14+%2B+1%2F17+=+%28%28+53%2F56+%29%29+%2F+t+
Multiply both sides by +17%2A56t+
+4%2A17t+%2B+56t+=+17%2A53+
+68t+%2B+56t+=+901+
+124t+=+901+
+t+=+901%2F124+ hrs
Strange result. Get another opinion. I may have
answered this twice. If so, sorry. I really think
my method is OK, though