Write an equation for each and solve. See Example 3 . Janice...

Write an equation for each and solve. See Example $3 .$ Janice and Blanca have to type a report on a project they did together. Janice could type it in $40 \mathrm{~min}$, and Blanca could type it in 1 hr. How long would it take them if they worked together?

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Key Concepts

Work Rate

Work rate problems involve determining the portion of a task that a worker can complete in one unit of time. Typically, the rate is represented as one divided by the time needed to finish the task, allowing us to quantify how fast a job gets done.

Combined Work Rates

When multiple agents work together, their individual work rates are added to form a combined work rate. This total rate represents the fraction of the task completed per unit time by all workers acting simultaneously.

Algebraic Equation Formulation

To solve work rate problems, you set up an equation where the combined work rate, multiplied by the time spent working together, equals one complete job. The equation effectively relates the rate, time, and task completion in a concise mathematical form.

Unit Consistency

Ensuring that all measurements use the same time unit is essential in these problems. Consistent units allow for accurate addition of individual work rates and proper calculation when solving for the total time required to complete the task.

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