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Question 765260: Please.. I need help
two people working together can do a job in 6 hours. if one of them works twice as fast as the other. How long would it take the faster person, working alone, to finish the same job?
Found 2 solutions by stanbon, DrBeeee:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! two people working together can do a job in 6 hours. if one of them works twice as fast as the other. How long would it take the faster person, working alone, to finish the same job?
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together rate::: 1/6 job/hr.
slower person rate: 1/(2x) job/hr.
faster person rate: 1/x job/hr.
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Equation:
rate + rate = together rate
1/x + 1/(2x) = 1/6
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Multiply thru by 6x:::
6 + 3 = x
x = 9 hrs (time for the slower person to do the job alone)
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Cheers,
Stan H.
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Answer by DrBeeee(684) (Show Source):
You can put this solution on YOUR website! Let x = the number of hours the first person takes to do the whole job alone.
Let y = the number of hours the second person takes to do the whole job alone.
When they work together it will take them n hours as given by the following formula:
(1) n = 1/(1/x + 1/y)
This is a very useful formula to use on this type of problem, put it in your file for future work.
In your problem we know two facts - just enough to solve for two unknowns, x and y.
Firstly we know that the total time it takes for the two people working together is 6 hours, therefore
(2) n = 6
The second fact is that one of them works twice as fast as the other, so that person takes one half the time as the other. Let's say that x is the faster worker, therefore we have
(3) x = y/2
Now put (2) and (3) into (1) to get
(4) 6 = 1/(2/y + 1/y) or
(5) 6 = y/(2 + 1) or
(6) 6 = y/3 or
(7) y = 18
So it takes the slower person 18 hours to do the job alone, whereas it only takes the faster person one half of this time or 9 hours.
Let's check this using the magic formula (1).
Is (6 = 1/(1/9 + 1/18))?
Is (6 = 1/(3/18))?
Is (6 = 18/3)?
Is (6 = 6)? Yes
Answer: The faster worker takes 9 hours to do the whole job alone.
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