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This activity is designed to encourage critical thinking on problems involving rates, specifically problems involving "working together".
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Work word problems tend to be rather difficult for dev math students and a domain where they typically memorize some "trick" (instead of an understanding of the problem situation) to setting up an equation that quickly fails with any variation in the problem context. This activity encourages students to think more deeply about combining rates and provides the teacher a nice flow for developing the desired equations in a meaningful way.