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Question 170889: Each valve A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves A and C open it takes 1.5 hours, and with only valves B and C open it takes 2 hours. How many hours will it take to fill the tank with only valves A and B open?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Each valve A, B, and C, when open, releases water into a tank at its own constant rate. With all three valves open, the tank fills in 1 hour, with only valves A and C open it takes 1.5 hours, and with only valves B and C open it takes 2 hours. How many hours will it take to fill the tank with only valves A and B open?
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time * rate = work done
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1(1/a + 1/b + 1/c) = 1
(3/2)(1/a + 1/c) = 1
2(1/b + 1/c) = 1
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1/a + 1/b + 1/c = 1
(3/2)(1/a) + 0 + (3/2)(1/c) = 1
0 + (2)(1/b) + (2)(1/c) = 1
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Use any method you know to solve this system to get:
1/a = 1/2
1/b = 1/3
1/c = 1/6
Comment: These are the rates at which each will fill do the job.
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A will take 2 hrs
B will take 3 hrs.
C will take 6 hours
Comment: These are the times each will take to do the job.
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Cheers,
Stan H.
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