To find a rational equation that determines the rate at which the coworker produces units, we start by identifying Tabitha's rate and the rate of her coworker.
Tabitha works at a rate of 1 unit every 10 hours, which gives her a rate of:
\[ R_T = \frac{1}{10} \text{ units per hour} \]
Let \( R_C \) be the rate (in units per hour) at which the coworker works. When they work together, they produce 1 unit in 5.24 hours, giving a combined rate of:
\[ R_{T+C} = \frac{1}{5.24} \text{ units per hour} \]
The relationship between their rates can be expressed as:
\[ R_T + R_C = R_{T+C} \]
Substituting the rates we know:
\[ \frac{1}{10} + R_C = \frac{1}{5.24} \]
To isolate \( R_C \), we can rewrite the equation:
\[ R_C = \frac{1}{5.24} - \frac{1}{10} \]
This rearrangement creates an equation that could be represented as a rational equation.
Among the options presented, the following equation aligns with this relationship:
\[ \frac{1}{10} + \frac{1}{x} = \frac{1}{5.24} \]
Where \( x \) represents the time in hours the coworker takes to produce 1 unit. Therefore, the correct model would be:
\[ \frac{1}{10} + \frac{1}{x} = \frac{1}{5.24} \]
So the correct response is:
Start Fraction 1 over 5.24 End Fraction plus Start Fraction 1 over x End Fraction equals Start Fraction 1 over 10 End Fraction