Question 139114: Three girls laura, Tammy, and jeri can wash the family cars clean the pool and mow the lawn in one hour and 20 minutes if jeri did all the work she would take twice as long as Tammy and 2 hours longer than laura how long would each girl take to the the jobs alone.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Three girls laura, Tammy, and jeri can wash the family cars clean the pool and mow the lawn in one hour and 20 minutes if jeri did all the work she would take twice as long as Tammy and 2 hours longer than laura how long would each girl take to the the jobs alone.
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Laura DATA:
Time = x hr/job ; Rate = 1/x job/hr
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Jeri DATA
Time = x+2 hr/job ; Rate = 1/(x+2) job/hr
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Tammy DATA:
Time = (x+2)/2 hr/job ; Rate = 2/(x+2) job/hr.
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Together DATA:
time = 4/3 hr/job ; Rate = 3/4 job/hr
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EQUATION:
rate + rate + rate = together rate
1/x + 1/(x+2) + 2/(x+2) = 3/4
Multiply thru by 4x(x+2) to get:
4(x+2) + 4x + 8x = 3x(x+2)
16x + 8 = 3x^2+6x
3x^2-10x-8 = 0
3x^2-12x+2x-8 = 0
3x(x-4)+2(x-4) = 0
(x-4)(3x+2) = 0
Positive answer:
x = 4 hrs. (time for Laura to do the job)
x+2=6 hrs. (time for Jeri to do the job)
(x+2)/2 = 3 hrs. (time for Tammy to do the job)
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Cheers,
Stan H.
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