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  3. Working alone at its constant rate, machine A produces k liters of a chemical in

Working alone at its constant rate, machine A produces k liters of a chemical in

游客2025-02-24  22
问题 Working alone at its constant rate, machine A produces k liters of a chemical in 10 minutes. Working alone at its constant rate, machine B produces k liters of the chemical in 15 minutes. How many minutes does it take machines A and B, working simultaneously at their respective constant rates, to produce k liters of the chemical?
______minutes
选项
答案 6
解析 Machine A produces k/10 liters per minute, and machine B produces k/15 liters per minute. So when the machines work simultaneously, the rate at which the chemical is produced is the sum of these two rates, which is liters per minute. To compute the time required to produce k liters at this rate, divide the amount k by the rate k/6 to get=6.
Therefore, the correct answer is 6 minutes(or equivalent).
One way to check that the answer of 6 minutes is reasonable is to observe that if the slower rate of machine B were the same as machine As faster rate of k liters in 10 minutes, then the two machines, working simultaneously, would take half the time, or 5 minutes, to produce the k liters. So the answer has to be greater than 5 minutes. Similarly, if the faster rate of machine A were the same as machine B’s slower rate of k liters in 15 minutes, then the two machines would take half the time, or 7.5 minutes, to produce the k liters. So the answer has to be less than 7.5 minutes. Thus the answer of 6 minutes is reasonable compared to the lower estimate of 5 minutes and the upper estimate of 7.5 minutes.
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 5: Simplify an Arithmetic or Algebraic Representation
Strategy 8: Search for a Mathematical Relationship
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