SOLUTION: Together Sophie and Clarissa can paint a house in 6 days. It takes Clarissa 5 days less than Sophie to paint the house by herself. How many days does it take Sophie to paint the ho
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Question 505214: Together Sophie and Clarissa can paint a house in 6 days. It takes Clarissa 5 days less than Sophie to paint the house by herself. How many days does it take Sophie to paint the house by herself? Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website! Together Sophie and Clarissa can paint a house in 6 days. It takes Clarissa 5 days less than Sophie to paint the house by herself. How many days does it take Sophie to paint the house by herself?
.
Let x = time (days) it takes for Sophie to do it alone
then
x-5 = time it takes for Clarissa
.
6(1/x + 1/(x-5)) = 1
multiplying both sides by x(x-5):
6(x-5 + x) = x(x-5)
6(2x-5) = x(x-5)
12x-30 = x^2-5x
-30 = x^2-17x
0 = x^2-17x+30
0 = (x-15)(x-2)
x = {15, 2}
the 2 won't make sense, throw it out leaving:
x = 15 days (Sophie's time)
.
Clarissa:
x-5 = 15-5 = 10 days
