Question 461620
Cindy can paint a house in 3 hr less time than Dustin. Together, it takes 18 hrs. How long does it take each to do the job by theirselves?
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Let x = time (hrs) it takes for Dustin
then
x-3 = time it takes for Cindy
.
18(1/x + 1/(x-3)) = 1
multiplying both sides by x(x-3):
18((x-3) + x) = x(x-3)
18(2x-3) = x^2-3x
36x-54 = x^2-3x
-54 = x^2-39x
0 = x^2-39x+54
solve by applying the "quadratic formula" to get:
x = {37.56, 1.44}
throw out the 1.44 (extraneous) to get
x = 37.56 hours (Dustin)
.
Cindy
x-3 = 37.56-3 = 34.56 hours
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Details of quadratic follows:
*[invoke quadratic "x", 1, -39, 54 ]