- Solve the following. See Examples I through 7. (Note: Some...

- Solve the following. See Examples I through 7. (Note: Some exercises can be modeled by equations without rational expressions.) It takes 9 hours for pump $A$ to fill a tank alone. Pump $B$ takes 15 hours to fill the same tank alone. If pumps $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ are used, the tank fills in 5 hours. How long does it take pump $\mathrm{C}$ to fill the tank alone?

- Solve the following. See Examples I through 7. (Note: Some exercises can be modeled by equations without rational expressions.)
It takes 9 hours for pump $A$ to fill a tank alone. Pump $B$ takes
15 hours to fill the same tank alone. If pumps $\mathrm{A}, \mathrm{B}$, and $\mathrm{C}$ are used, the tank fills in 5 hours. How long does it take pump $\mathrm{C}$ to fill the tank alone?

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Key Concepts

Setting Up and Solving Equations

In work problems, equations are formulated by equating the sum of the individual work rates to the overall work rate required to complete the task. These equations often involve rational expressions due to the reciprocal relationship between time and rate, and solving them requires skills in algebraic manipulation.

Work Rates

Work rates represent the portion of a task completed per unit of time, typically expressed as the reciprocal of the total time needed to finish the task. This concept is used to quantify the efficiency of agents completing work and is fundamental in problems where individual contributions must be compared or combined.

Combined Work Rates

When multiple agents work together on a task, their individual work rates add up to form a combined work rate. This approach allows one to determine the time required to complete a task when several agents are involved, as the total work done per unit time is the sum of their individual work contributions.

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