SOLUTION: working together, two crews can clear snow from the city's streets in 20 hours.working alone the faster crew requires 9 hours less time than the slower crew. How many hours would i

Question 433470: working together, two crews can clear snow from the city's streets in 20 hours.working alone the faster crew requires 9 hours less time than the slower crew. How many hours would it take each crew to clear the streets working alone?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
working together, two crews can clear snow from the city's streets in 20 hours.
working alone the faster crew requires 9 hours less time than the slower crew.
How many hours would it take each crew to clear the streets working alone?
:
x = time required by the faster crew
then
(x+9) = time required by the slow pokes
:
Let the completed job = 1; (snow-free streets)
:
+ = 1
Multiply by x(x+9), results
20(x+9) + 20x = x(x+9)
:
20x + 180 + 20x = x^2 + 9x
:
40x + 180 = x^2 + 9x
:
0 = x^2 + 9x - 40x - 180
A quadratic equation
x^2 - 31x - 180 = 0
This will factor to
(x-36)(x+5) = 0
the positive solution
x = 36 hrs required by the faster crew
the
36 + 9 = 45 hrs required by the slow pokes
:
:
Check this
20/36 + 20/45 =
.56 + .44 = 1.0
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