SOLUTION: Two pumps can fill a water tank in 104 minutes when working together. Alone, the second pump takes 2 times as long as the first to fill the tank. How many minutes does it take the
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-> SOLUTION: Two pumps can fill a water tank in 104 minutes when working together. Alone, the second pump takes 2 times as long as the first to fill the tank. How many minutes does it take the
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Question 538094: Two pumps can fill a water tank in 104 minutes when working together. Alone, the second pump takes 2 times as long as the first to fill the tank. How many minutes does it take the first pump alone to fill the tank?
You can put this solution on YOUR website! 1/A = pump 1's rate of filling the tank per min.
1/B = pump 2's rate of filling the tank per min.
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(1/A+1/B)*104 min = 1 filled tank = 1 whole job done
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A can do the work twice as fast as B.
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1/A = 2/B
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substitute
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(2/B + 1/B) * 104 = 1
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3/B * 104 = 1
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312/B = 1
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cross multiply
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312 = B
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B can fill the tank in 312 min.
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B does 1/312 of the job per min.
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1/A = 2/312 = 1/156
or
A can do the job in 156 min.
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Check by determine how much of the tank each can fill in 104 min.
1/312 * 104 = 104/312 = 1/3
1/156 * 104 = 104/156 = 2/3
1/3 + 2/3 = 1 filled tank
Correct.
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Answer: The first pump can fill the tank in 156 minutes working alone.
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