SOLUTION: Mark can mow a lawn in 20 minutes less than his sister Marie. Together they can mow the lawn in 24 minutes. How long would it take Marie to finish the mowing if she worked alone?

Question 679020: Mark can mow a lawn in 20 minutes less than his sister Marie. Together they can mow the lawn in 24 minutes. How long would it take Marie to finish the mowing if she worked alone?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
Mark can mow a lawn in 20 minutes less than his sister Marie. Together they can mow the lawn in 24 minutes. How long would it take Marie to finish the mowing if she worked alone?
.
Let x = time (mins) it takes Marie
then
x-20 = time (mins) it takes Mark
.
24(1/x + 1/(x-20)) = 1
multiplying both sides by x(x-20):
24((x-20) + x) = x(x-20)
24(2x-20) = x^2-20x
48x-480 = x^2-20x
-480 = x^2-68x
0 = x^2-68x+480
0 = (x-8)(x-60)
x = {8,60}
throw out 8 (extraneous) leaving:
x = 60 minutes

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