Question 128327
Working alone, Anton can install a brick patio in 2 hours less than Bill. Together Anton and Bill can install the patio in 4 hours. To the nearest tenth of an hour, how long does it take Bill to install the patio working alone?
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Bill DATA:
Time = x hrs/job ; Rate = 1/x job/hr
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Anto DATA:
Time = (x-2) hrs/job ; Rate = 1/(x-2) job/hr
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Together DATA:
Time = 4 hrs/job ; Rate = 1/4 job/hr
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EQUATION:
rate + rate = together rate
1/x + 1/(x-2) = 1/4
Multiply thru by 4x(x-2) to get:
4(x-2) + 4x = x(x-2)
8x - 8 = x^2-2x
x^2-10x+8 = 0
x = [10 +- sqrt(100-4*8)]/2
x = [10 +- sqrt(68)]/2
Positive answer:
x = (10 + sqrt(68))/2
x = 9.1231 hrs (Time is takes Bill to do the job)
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Cheers,
Stan H.