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| Math Central | Quandaries & Queries |
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Question from Dee, a student: I have a few questions that im have trouble working out... 1. One number is three times another number; if each is increased by 1 the sum of the reciprocals is 10/21. Find the numbers 2.A tank can be filled by 2 pipes together in 6 hours; if the larger pipe alone takes 5 hours less than the smaller to fill the tank, find the time in which each pipe alone would fill the tank |
Dee,
Each of these problems involve reciprocals. It is explicit in the first problem. Suppose the two numbers are x and y then one is three times the other so I can say y = 3x. The second fact you are told is that if each is increased by 1 (so the numbers would be x + 1 and y + 1) then the sum of the reciprocals is 10/21. Thus
1/(x + 1) + 1/(y + 1) = 10/21
Use the expression y = 3x to write this equation in terms of the one variable x. Add the fractions on the left side and solve for x.
I hope this helps,
Penny
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