SOLUTION: It takes a boy 15 minutes longer to mow a lawn than it takes his sister. If they work together, it takes them 56 minutes. How long does it take the boy to mow the lawn by himself?

Question 600040: It takes a boy 15 minutes longer to mow a lawn than it takes his sister. If they work together, it takes them 56 minutes. How long does it take the boy to mow the lawn by himself?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
It takes a boy 15 minutes longer to mow a lawn than it takes his sister. If they work together, it takes them 56 minutes. How long does it take the boy to mow the lawn by himself?
.
Let x = time (minutes) it takes for sister to mow lawn by herself
then
x+15 = time (minutes) for boy
.
56(1/x + 1/(x+15)) = 1
56((x+15) + x) = x(x+15)
56(2x+15) = x^2+15x
112x+840 = x^2+15x
840 = x^2-97x
0 = x^2-97x-840
0 =(x-105)(x+8)
x = {-8, 105}
throw out negative solution (extraneous)leaving:
x = 105 minutes (sister)
.
Boy:
x+15 = 105+15 = 120 minutes
or
2 hours

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