Question 644822
    Alfred, Mindy and Casey can mow their lawn in 60 minutes if they work together. If it takes Alfred twice as long as Mindy and Casey take 10 minutes more than Mindy, how long would it take each to mow the lawn alone? 
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Let m = time (mins) it takes Mindy to mow alone
then
2m = time (mins) it takes Alfred to mow alone
m+10 = time (mins) it takes Casey to mow alone
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from:"Alfred, Mindy and Casey can mow their lawn in 60 minutes if they work together." we get our equation:
60(1/m + 1/(2m) + 1/(m+10)) = 1
multiplying both sides by m(2m)(m+10) we get:
60((2m)(m+10) + m(m+10) + m(2m)) = m(2m)(m+10)
60(2m^2+20m + m^2+10m + 2m^2) = (2m^2)(m+10)
60(5m^2+30m) = 2m^3+20m^2
30(5m^2+30m) = m^3+10m^2
150m^2+900m = m^3+10m^2
900m = m^3-140m^2
0 = m^3-140m^2-900m
0 = m(m^2-140m-900)
applying the quadratic formula, we get:
m = {0, 146.16, -6.16}
toss out 0 and the negative solution (extraneous) leaving:
m = 146 mins (Mindy)
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Alfred:
2m = 2(146) = 292 mins
Casey:
m+10 = 146+10 = 156 mins
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Details from quadratic formula:
*[invoke quadratic "x", 1, -140, -900 ]