SOLUTION: It takes Ralph 6 hours to paint a fence. Lisa can do the same job in 10 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work together to

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: It takes Ralph 6 hours to paint a fence. Lisa can do the same job in 10 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work together to       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 723201: It takes Ralph 6 hours to paint a fence. Lisa can do the same job in 10 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work together to finish painting the fence? Give your answer to three decimal places.




Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The question to ask is: "What fraction of the job does
Ralph get done in a 1/2 hour ?"
------------------
Multiply Ralph's rate of painting times 1/2 hr
( 1 fence / 6 hrs ) x ( 1/2 ) = 1/12
So Ralph finishes 1/12 of the fence in 1/2 hr
---------------
There is 11/12 of the fence left to paint
Add their rates of painting to get their rate
painting 11/12 of the fence
+1%2F6+%2B+1%2F10+=+%2811%2F12%29+%2F+t+
Multiply both sides by +12t+
+2t+%2B+1.2t+=+11+
+3.2t+=+11+
+t+=+11%2F3.2+
+t+=+3.438+
They must work together for 3.438 hrs to finish