Machine A, working alone at its constant rate, produces x pounds of peanut butte

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问题 Machine A, working alone at its constant rate, produces x pounds of peanut butter in 12 minutes. Machine B, working alone at its constant rate, produces x pounds of peanut butter in 18 minutes. How many minutes will it take machines A and B, working simultaneously at their respective constant rates, to produce x pounds of peanut butter?
______minutes

选项

答案 7.2

解析 Translating the given information into an algebraic expression, you see that machine A produces x/12 pounds of peanut butter in 1 minute, and machine B produces x/18 pounds of peanut butter in 1 minute. Therefore, working simultaneously, machine A and machine B produce

pounds of peanut butter in 1 minute.
Letting t be the number of minutes it takes machines A and B, working simultaneously, to produce x pounds of peanut butter, you can set up the following equation.

Solving for t, you get

The correct answer is 7.2.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship

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