SOLUTION: 2 landscape workers can complete a certain job in a total of 20 hours. Working alone, one can do this same job in 2 hours less time than it takes the other worker. How long would

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: 2 landscape workers can complete a certain job in a total of 20 hours. Working alone, one can do this same job in 2 hours less time than it takes the other worker. How long would       Log On


   

Question 1112768: 2 landscape workers can complete a certain job in a total of 20 hours. Working alone, one can do this same job in 2 hours less time than it takes the other worker. How long would it take the faster worker to do the job if the slower worker is unable to work?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
1%2Fx%2B1%2F%28x-2%29=1%2F20
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20%28x-2%29%2B20x=x%28x-2%29
20x-40%2B20x=x%5E2-2x
40x-40=x%5E2-2x
x%5E2-42x%2B40=0
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x=%2842%2B-+sqrt%2842%5E2-4%2A40%29%29%2F2
x=%2842%2B-+sqrt%281604%29%29%2F2
x=%2842%2B-+2%2Asqrt%28401%29%29%2F2
x=21%2B-+sqrt%28401%29
nearstwholehour,x=41

Faster worker: 39 hours
Slower worker: 41 hours

check:
1%2F41%2B1%2F39
0.02439%2B0.02564
0.05003=1%2F20approx