SOLUTION: When workers A and B work together, they can finish the flooring of a house in 6 days.When worker A works alone, he takes 5 days less than worker B to finish the flooring of the ho

Algebra ->  Rate-of-work-word-problems -> SOLUTION: When workers A and B work together, they can finish the flooring of a house in 6 days.When worker A works alone, he takes 5 days less than worker B to finish the flooring of the ho      Log On


   

Question 1002532: When workers A and B work together, they can finish the flooring of a house in 6 days.When worker A works alone, he takes 5 days less than worker B to finish the flooring of the house. How many days does worker A and worker B needs to finish the flooring of the house if they work alone?
Found 2 solutions by josgarithmetic, stanbon:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
WORKER        RATE in JOB/DAY
A              1/(x-5)
B              1/x
A&B            1/6

The rate of agents acting together on the same job is the sum of the individual rates.

highlight%281%2F%28x-5%29%2B1%2Fx=1%2F6%29
Find the value or solve for x.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
When workers A and B work together, they can finish the flooring of a house in 6 days.When worker A works alone, he takes 5 days less than worker B to finish the flooring of the house. How many days does worker A and worker B needs to finish the flooring of the house if they work alone?
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Together rate:: 1/6 job/day
Worker B rate:: 1/x job/day
Worker A rate:: 1/(x-5) job/day
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Equation:
rate + rate = together rate
1/x + 1/(x-5) = 1/6
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6(x-5) + 6x = x(x-5)
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12x - 30 = x^2 - 5x
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x^2 -17x + 30 = 0
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(x-15)(x-2) = 0
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Realistic answer:
x = 15
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B time = x = 15 days to do the job alone
A time = x-5 = 10 days to do the job alone
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Cheers,
Stan H.
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