Solve using rational functions. An experienced employee can enter tax data into a computer twice as fast as a new employee. Working together, it takes the employees 2 hours. How long will it take the experienced employee working alone?

Let \( x \) be the time it takes the experienced employee to enter the tax data working alone, in hours. Since the experienced employee works twice as fast as the new employee, the new employee's time to complete the same task alone would be \( 2x \) hours.

### Step 1: Define the rates of work.
- The experienced employee works at a rate of \( \frac{1}{x} \) of the job per hour.
- The new employee works at a rate of \( \frac{1}{2x} \) of the job per hour.

### Step 2: Combine their rates when they work together.
When both employees work together, their combined rate is:
\[
\frac{1}{x} + \frac{1}{2x}
\]

This simplifies as follows:
\[
\frac{1}{x} + \frac{1}{2x} = \frac{2}{2x} + \frac{1}{2x} = \frac{3}{2x}
\]

### Step 3: Set up the equation based on the combined rate.
We know that working together, the job is completed in 2 hours,

An experienced employee can enter tax data into a computer twice as fast as a new employee. Working together, it takes the employees 2 hours. How long will it take the experienced employee working alone?

This guide provides a step-by-step solution to a work rate problem using rational functions. Learn how to calculate how long it takes for an experienced employee to complete a task alone, given that they work twice as fast as a new employee and together they finish in 2 hours. Suitable for Grades 9-12.

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