SOLUTION: Rusty and Nancy Brauner are planting flats of spring flowers. Working alone, Rusty would take 2 hr longer than Nanvy to plant the flowers. Working together, they do the job in 12 h
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Question 888060: Rusty and Nancy Brauner are planting flats of spring flowers. Working alone, Rusty would take 2 hr longer than Nanvy to plant the flowers. Working together, they do the job in 12 hr. How long would it have taken each person working alone? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Rusty and Nancy Brauner are planting flats of spring flowers. Working alone, Rusty would take 2 hr longer than Nanvy to plant the flowers. Working together, they do the job in 12 hr. How long would it have taken each person working alone?
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Nancy DATA:
time = x hrs/job ; rate = 1/x job/hr
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Rusty DATA:
time = x+2 hrs/job ; rate = 1/(x+2) job/hr
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Together DATA:
time = 12 hr/job ; rate = 1/12 job/hr
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Equation:
rate + rate = together rate
1/x + 1/(x+2) = 1/12
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12(x+2) + 12x = x(x+2)
12x + 24 + 12x = x^2 + 2x
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x^2 - 22x -24 = 0
x = [22 +- sqrt(22^2-4*-24)]/2
Positive solution:
x = 23.04 hrs (Nancy time to do the job)
x+2 = 25.04 hrs (Rusty time to do the job)
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Cheers,
Stan H.
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