SOLUTION: It takes Richard 39 minutes longer to do a job than it takes Katie to do the same job. Working together they can do the job in 40 minutes. How long will it take Richard and Katie
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Question 928649: It takes Richard 39 minutes longer to do a job than it takes Katie to do the same job. Working together they can do the job in 40 minutes. How long will it take Richard and Katie to each do the job alone? Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! It takes Richard 39 minutes longer to do a job than it takes Katie to do the same job. Working together they can do the job in 40 minutes. How long will it take Richard and Katie to each do the job alone?
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Together rate = 1/40 job/min
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Katie rate = 1/x job/min
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Richard rate = 1/(x+39) job/min
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Equation:
rate + rate = together rate::
1/x + 1/(x+39) = 1/40
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40(x+39) + 40x = x(x+39)
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40x + 40*39 + 40x = x^2 + 39x
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x^2 -41x - 40*39 = 0
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x = 65 minutes (time for Katie to do the job)
x+39 = 104 minutes (time for Richard to do the job)
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Cheers,
Stan H.
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