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)

Question

Responses

15.24+1x=110
Start Fraction 1 over 5.24 End Fraction plus Start Fraction 1 over x End Fraction equals Start Fraction 1 over 10 End Fraction

15.24+110=1x
Start Fraction 1 over 5.24 End Fraction plus Start Fraction 1 over 10 End Fraction equals Start Fraction 1 over x End Fraction

110+1x=15.24
Start Fraction 1 over 10 End Fraction plus Start Fraction 1 over x End Fraction equals Start Fraction 1 over 5.24 End Fraction

x10=15.24

Answer 1

To find a rational equation that determines the rate at which Tabitha's coworker produces units, we can use the concept of rates of work.

Let’s define:

• \( r_T \) = rate of Tabitha = 1 unit / 10 hours = \( \frac{1}{10} \) units per hour
• \( r_C \) = rate of the coworker (the unknown we want to find) = \( \frac{1}{x} \) units per hour, where \( x \) is the time in hours it takes the coworker to make 1 unit.

When working together, their combined rate is: \[ r_T + r_C = \frac{1}{5.24} \]

This gives us the equation: \[ \frac{1}{10} + \frac{1}{x} = \frac{1}{5.24} \]

Now let's compare it with the options provided:

1. \( 15.24 + 1x = 110 \)
2. \( \frac{1}{5.24} + \frac{1}{x} = \frac{1}{10} \)
3. \( 110 + 1x = 15.24 \)
4. \( \frac{1}{10} + \frac{1}{x} = \frac{1}{5.24} \)
5. \( x10 = 15.24 \)

The correct choice that represents the derived equation is: 4. \( \frac{1}{10} + \frac{1}{x} = \frac{1}{5.24} \).