Official Guide Explanation:
Problem Solving #16

Background

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Solution and Metadata

Question: 16
Page: 64
Difficulty: 5 (Moderate)
Category 1: Word Problems > Work Problems > 3+ inputs
Category 2: Arithmetic > Fractions >

Explanation: If you want the greatest part of the job to be done in an hour, you want to use the two machines that work the fastest: the ones that can get the job done in 4 and 5 hours, respectively. In one hour, those machines can get (1/4) and (1/5) of the job done, respectively. Combined, they can complete (1/4) + (1/5) = (5/20) + (4/20) = (9/20) of the job in one hour, choice (B).

Alternatively, you can use the equation ((AB)/(A + B)), where A and B are the amounts of time it requires each machine to do the job. In that case, the total amount of time required for those two machines to do the job is ((4(5))/(4 + 5)) = (20/9) hours. If it takes (20/9) hours to do the job, the machines can get the inverse, (9/20) of the job done in one hour.

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