Tabitha works at a rate of 1 unit every 10 hours. Working together with a coworker, it only takes 5.24 hours to make 1 unit. Which of the following models is a rational equation that could determine the rate at which the coworker produces units?

Question

1. x/10=1/5.24
2. 1/10+1/x=1/5.24
3. 1/5.24+1/10=1/x
4. 1/5.24+1/x+1/10

Answer 1

To solve this problem, we need to model the rates at which Tabitha and her coworker produce units.

Let \( x \) be the rate (in units per hour) at which the coworker works.

Tabitha works at a rate of: \[ \frac{1 \text{ unit}}{10 \text{ hours}} = \frac{1}{10} \text{ units/hour} \]

When working together, they produce 1 unit in 5.24 hours, so their combined rate is: \[ \frac{1 \text{ unit}}{5.24 \text{ hours}} = \frac{1}{5.24} \text{ units/hour} \]

The formula for their combined rates can be expressed as: \[ \text{Rate of Tabitha} + \text{Rate of Coworker} = \text{Combined Rate} \] or more specifically: \[ \frac{1}{10} + \frac{1}{x} = \frac{1}{5.24} \]

This matches option (2). Thus, the correct rational equation that could determine the rate at which the coworker produces units is:

2. \( \frac{1}{10} + \frac{1}{x} = \frac{1}{5.24} \)