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)
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
The correct answer is 3. 1/5.24+1/10=1/x.
The correct option is 3. 1/5.24 + 1/10 = 1/x. This is a rational equation that could be used to determine the rate at which the coworker produces units when working together with Tabitha.
To determine the rate at which the coworker produces units, we need to set up a rational equation and solve for x.
Let's examine the given information:
- Tabitha works at a rate of 1 unit every 10 hours.
- When Tabitha and her coworker work together, it takes 5.24 hours to make 1 unit.
We want to find the rate at which the coworker produces units, so let's represent that with x units per hour.
The equation that represents the situation is:
1/10 + 1/x = 1/5.24
Now, let's look at the options provided:
1. x/10 = 1/5.24
This equation does not match the information given because it is not in the form mentioned above.
2. 1/10 + 1/x = 1/5.24
This equation matches the information given and is in the correct form. Each term represents the rate of work for Tabitha and the coworker. This is the correct answer.
3. 1/5.24 + 1/10 = 1/x
This equation does not match the information given because the terms are in a different order. The equation is also not in the correct form.
4. 1/5.24 + 1/x + 1/10
This equation does not match the information given because it has an additional term at the end. The equation is not in the correct form.
Therefore, the correct option is 2. 1/10 + 1/x = 1/5.24, which represents the rate at which the coworker produces units.