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#mathematics
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#mathematics-grade-11
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#problem-solving
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Two pipes can fill a tank in 6 hour. The large pipe works twice as fast as the smaller pipe. How long would it take each pipe to fill the tank if they worked separately
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Two pipes can fill a tank in 6 hour. The large pipe works twice as fast as the smaller pipe. How long would it take each pipe to fill the tank if they worked separately
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Nov 29, 2023
Let x be the time it takes for the smaller pipe to fill the tank. Therefore, the larger pipe takes x/2 time to fill the tank. The rate of the smaller pipe is 1/x of the tank per hour. The rate of the larger pipe is 1/(x/2) = 2/x of the tank per hour. Together, the rate of both pipes is 1/x + 2/x = 3/x of the tank per hour. Since they can fill the tank in 6 hours, their combined rate is 1/6 of the tank per hour. Therefore, 3/x = 1/6. Multiplying both sides by 6x, we get 18 = x. Thus, it takes the smaller pipe 18 hours to fill the tank. The larger pipe takes 18/2 = <<18/2=9>>9 hours to fill the tank. Answer: \boxed{18, 9}.