Question 250410
Three workers are to accomplish a job. The first worker can finish the job in 7 hours. The second worker can finish the job in 6 hours. The third worker can finish the job in x hours. The three workers can finish the job in 2 hours if they work together. Find x.
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Equation:
rate + rate + rate = together rate
1/7 + 1/6 + 1/x = 1/2
Multiply thru by 42x:
6x + 7x + 42 = 21x
42 = 8x
x = 21/4 = 5 1/4 hours (time the 3rd worker takes to do the job)
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also 
A pond has an inlet to fill it up and an outlet to drain it. The inlet can fill it in 3 hours and the the outlet can drain it in 9 hours. Suppose the pond was empty and the person in charge of filling it up opened the inlet but forgot to close the outlet. After 2 hours, he realized that the outlet is still open. At that time, he closed the outlet. How long did it take for the pond to get filled after the outlet was closed?
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Inlet pipe rate: 1/3 job/hr
Outlet pipe rate: 1/9 job/hr
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Work done in 2 hours.
2(1/3 + 1/9) = 2(3/9+1/9) = 2(4/9) = 8/9 of the job
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Time to finish the job
x(1/3) = (1/9) job
x = 3(1/9) = 1/3 hr. (time to fill 1/9 of the job and fill the pool)
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Cheers,
Stan H.