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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?(1 point)%0D%0AResponses%0D%0A%0D%0A110+1x=15.24%0D%0AStart Fraction 1 over 10 End Fraction plus Start Fraction 1 over x End Fraction equals Start Fraction 1 over 5.24 End Fraction%0D%0A%0D%0A15.24+110=1x%0D%0AStart Fraction 1 over 5.24 End Fraction plus Start Fraction 1 over 10 End Fraction equals Start Fraction 1 over x End Fraction%0D%0A%0D%0A15.24+1x=110%0D%0AStart Fraction 1 over 5.24 End Fraction plus Start Fraction 1 over x End Fraction equals Start Fraction 1 over 10 End Fraction%0D%0A%0D%0Ax10=15.24

1 answer

To find the rate at which Tabitha's coworker produces units, let's first analyze the given information:

  1. Tabitha works at a rate of \( \frac{1 \text{ unit}}{10 \text{ hours}} \), which means her rate is \( \frac{1}{10} \) units per hour.
  2. Together with her coworker, they produce 1 unit in 5.24 hours, giving them a combined rate of \( \frac{1}{5.24} \) units per hour.

Let \( x \) represent the rate (in units per hour) at which the coworker works. The combined rates of both Tabitha and her coworker can be expressed as:

\[ \frac{1}{10} + \frac{1}{x} = \frac{1}{5.24} \]

This equation correctly models the situation.

Now, let's look at the options provided. The valid rational equation is:

Start Fraction 1 over 10 End Fraction plus Start Fraction 1 over x End Fraction equals Start Fraction 1 over 5.24 End Fraction.

So the final answer is: Start Fraction 1 over 10 End Fraction plus Start Fraction 1 over x End Fraction equals Start Fraction 1 over 5.24 End Fraction.