Official Guide Explanation:
Problem Solving #213




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Solution and Metadata

Question: 213
Page: 183
Difficulty: 7 (Very Difficult)
Category 1: Algebra > Equations >
Category 2: Word Problems > Work Problems > 2 inputs
Category 3: Arithmetic > Fractions >

Explanation: If the reciprocal of r is equal to the sum of the reciprocals of x and y, we can write an equation as follows:

(1/(r)) = (1/(x)) + (1/(y))

(1/(r)) = ((y)/(xy)) + ((x)/(xy)) = ((x + y)/(xy))

r = ((xy)/(x + y)), choice (D).

You may notice that this is the same equation as the one for combined rate, where x and y stand in for the individual rates, and r is equivalent to the combined rate.

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