SOLUTION: It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 16 hours. If Ralph paints alone for 25 minutes before Lisa begins helping, how long must they work toget

Question 854340: It takes Ralph 14 hours to paint a fence alone. Lisa can do the same job in 16 hours. If Ralph paints alone for 25 minutes before Lisa begins helping, how long must they work together to finish painting the fence? Give your answer as a simplified fraction.
Found 3 solutions by richwmiller, Vladdroid, josmiceli:
Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
25/60/14+x/14+x/16=1
5/168+15x/112 = 1
x = 326/45
x = 7.2444
just about 7 hours 15 minutes together.
Answer by Vladdroid(91)   (Show Source): You can put this solution on YOUR website!
25/60/14+x/14+x/16=1
5/168+15x/112 = 1
x = 326/45
x = 7.2444
just about 7 hours 15 minutes together.
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Ralph's rate of painting is:
( 1 fence ) / ( 14 hrs )
He paints the fence alone for hr
I can say:
( fraction of the fence he paints ) = ( his rate of painting ) x ( time spent painting )
fraction of the fence he paints =
That means there is
of the fence left to paint
------------------------
Let = the time in hours for them to paint
of the fence painting together
Add their rates of painting to find rate painting together

Multiply both sides by

hrs
and
min
--------------------------
Working together, they finish the fence in 7 hrs 14 min 40 sec
As a simplified fraction, expressed in hours, this is:
hrs
--------------------------
check answer using calculator:

OK

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