<PRE><B>Question 640690</B>
Jack can paint a house twice as fast as Jill. Jill starts at 8 AM, Jacj joins in at 10 AM. They finished at 2 PM. How long does it take each of them to paint the house by themself?
.
Let x = time (hours) it takes for Jack to paint house
then
2x = time (hours) it takes for Jill to paint house
.
Jill has a 2 hour head start
then, they both paint for an additional 4 hours
.
2(1/(2x)) + 4(1/x + 1/(2x)) = 1
multiplying both sides by 2x:
2(1) + 4(2 + 1) = 2x
2 + 4(3) = 2x
2 + 12 = 2x
14 = 2x
7 hours = x (time it takes for Jack to paint the house alone)
.
Jill:
2x = 2(7) = 14 hours
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