SOLUTION: It takes Ralph 13 hours to paint a fence. Lisa can do the same job in 9 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work together to

Question 789061: It takes Ralph 13 hours to paint a fence. Lisa can do the same job in 9 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 ptaylor(2198) (Show Source): You can put this solution on YOUR website!

Let x=amount of time needed for them to finish the fence working together
Ralph paints at the rate of 1/13 of the fence per hour
Lisa paints at the rate of 1/9 of the fence per hour
Together they paint at the rate of 1/13 +1/9=9/117 +13/117=22/117 of the fence per hour
In 30 min (1/2 hr) Ralph paints (1/2)(1/13)=1/26 of the fence leaving 25/26 of the fence to be painted
Now (22/117)*x=25/26 is the equation that we need to solve. The rate at which they work (22/117) times the time needed equals the amount of fence that remains to be painted (25/26) of 1 fence.
Multiply each side by (26)(117)
22*26*x=25*117
572x=2925
x=5.114 hrs
Hope this helps---ptaylor

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