1Cademy - Solving a Work Application: Weeding a Garden

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Rational Equation

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Solving a Work Application: Weeding a Garden

Apply the problem-solving strategy for work applications to find the time needed for two people to weed a garden together. If Daria takes $7$ hours alone and her mother takes $3$ hours alone, let $t$ be the hours needed together. Their hourly rates are $\frac{1}{7}$ and $\frac{1}{3}$ , respectively, and their combined hourly rate is $\frac{1}{t}$ . The rational equation is: $\frac{1}{7} + \frac{1}{3} = \frac{1}{t}$ Multiply both sides by the LCD, $21t$ : $21t \left(\frac{1}{7} + \frac{1}{3}\right) = 21t \left(\frac{1}{t}\right)$ Distribute and simplify: $3t + 7t = 21$ $10t = 21$ $t = \frac{21}{10}$ Converting to a mixed number gives $2 \frac{1}{10}$ hours. Since $\frac{1}{10}$ of an hour is $6$ minutes, it will take them $2$ hours and $6$ minutes working together.

Updated 2026-05-01

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OpenStax Intermediate Algebra

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