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Question 667792: "Work" word problem: Painting a House
Donald and Ken are painting a house this summer. Donald worked alone for 9 days. The next day Ken joined Donald to work on the house. Working together, they finished the house in 6 more days. If Ken could have painted the entire house in 22 days, how many days would it have taken Donald to paint the house alone. round the answer to the nearest whole number, if necessary.
Possible answers are: a) 21 b) 25 c) 30 d) 12
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Painting a House
Donald and Ken are painting a house this summer.
Donald worked alone for 9 days. The next day Ken joined Donald to work on the house.
Working together, they finished the house in 6 more days.
If Ken could have painted the entire house in 22 days, how many days would it have taken Donald to paint the house alone.
round the answer to the nearest whole number, if necessary.
:
Let d = time required by Donald to paint the house alone
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Let the completed job = 1
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Each will do a fraction of the job, the two fractions must add up to 1
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From the given information we know that Donald worked 15 days, Ken worked 6
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The shared work equation
 +  = 1
multiply by 22d, to clear the denominators, results:
22(15) + 6d = 22d
330 = 22d - 6d
330 = 16d
d = 330/16
d = 20.625 ~ 21 days for Donald to do the job alone
:
:
Confirm this
15/20.625 + 6/22 =
.73 + 27 = 1
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