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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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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?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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