Math CentralQuandaries & Queries


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


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,

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