1Cademy - Solving a Work Application: Painting a Room

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Rational Equation

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Solving a Work Application: Painting a Room

Apply the problem-solving strategy for work applications to find the combined time for two people to paint a room. If Pete takes $10$ hours alone and Alicia takes $8$ hours alone, let $t$ be the hours needed together. In $1$ hour, Pete paints $\frac{1}{10}$ of the room, Alicia paints $\frac{1}{8}$ , and together they paint $\frac{1}{t}$ . The rational equation is: $\frac{1}{10} + \frac{1}{8} = \frac{1}{t}$ Multiply both sides by the LCD, $40t$ : $40t \left(\frac{1}{10} + \frac{1}{8}\right) = 40t \left(\frac{1}{t}\right)$ Distribute and simplify: $4t + 5t = 40$ $9t = 40$ $t = \frac{40}{9}$ Converting the improper fraction to a mixed number yields $4 \frac{4}{9}$ hours. To convert the fractional hour to minutes, multiply by $60$ and round to the nearest minute to get $27$ minutes. It would take Pete and Alicia about $4$ hours and $27$ minutes working together.

Updated 2026-05-01

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OpenStax Intermediate Algebra

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