1Cademy - Solving a Work Application: Mowing a Golf Course

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Rational Equation

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Solving a Work Application: Mowing a Golf Course

Apply the problem-solving strategy for work applications to find the time needed for two gardeners to mow a golf course together. If one gardener takes $4$ hours alone and another takes $6$ hours alone, let $t$ be the hours needed together. Their hourly rates are $\frac{1}{4}$ and $\frac{1}{6}$ , respectively, and their combined hourly rate is $\frac{1}{t}$ . The rational equation is: $\frac{1}{4} + \frac{1}{6} = \frac{1}{t}$ Multiply both sides by the LCD, $12t$ : $12t \left(\frac{1}{4} + \frac{1}{6}\right) = 12t \left(\frac{1}{t}\right)$ Distribute and simplify: $3t + 2t = 12$ $5t = 12$ $t = \frac{12}{5}$ Converting to a mixed number gives $2 \frac{2}{5}$ hours. Since $\frac{2}{5}$ of an hour is $24$ minutes, it would take the two gardeners $2$ hours and $24$ minutes working together.

Updated 2026-05-01

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OpenStax Intermediate Algebra

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