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?
Let's assume the rate at which the coworker produces units is r units per hour.
According to the given information, Tabitha can produce 1 unit every 10 hours, so her rate is 1/10 units per hour.
When working together, Tabitha and her coworker can produce 1 unit in 5.24 hours.
Using the formula for working together: 1/10 + r = 1/5.24
To get the rational equation, we can rearrange the equation: r = 1/5.24 - 1/10
Therefore, the rational equation that could determine the rate at which the coworker produces units is r = 1/5.24 - 1/10.
Let's assume that the coworker's rate is "x" units per hour.
According to the given information, Tabitha works at a rate of 1 unit every 10 hours. This can be expressed as 1 unit per 10 hours or 1/10 units per hour.
When Tabitha and the coworker work together, it takes them 5.24 hours to make 1 unit.
We can express the combined rate of Tabitha and the coworker as 1 unit per 5.24 hours or 1/5.24 units per hour.
Using this information, we can set up the following rational equation to determine the coworker's rate:
1/10 + x = 1/5.24
Simplifying this equation, we get:
x + 1/10 = 1/5.24
Now, we can solve for "x":
x = 1/5.24 - 1/10
Simplifying further, we get:
x = (10 - 5.24) / (52.4)
Thus, the rational equation that could determine the rate at which the coworker produces units is:
x = 4.76 / 52.4.
To determine the rate at which Tabitha's coworker produces units, we need to set up a rational equation based on the given information.
Let's assume that the coworker's rate is represented by 'x' units per hour.
According to the problem, Tabitha works at a rate of 1 unit every 10 hours. This can be represented as 1 unit / 10 hours.
When they work together, it only takes 5.24 hours to make 1 unit. So, the combined work rate is 1 unit / 5.24 hours.
Now we can set up the rational equation:
1/10 + x = 1/5.24
This equation represents the combined work rate of Tabitha and her coworker. To find the rational equation that determines the coworker's rate, we need to rearrange the equation:
x = 1/5.24 - 1/10
Simplifying this expression, we get:
x = (10 - 5.24) / (5.24 * 10)
x = 4.76 / 52.4
Therefore, the rational equation that could determine the rate at which the coworker produces units is:
x = 0.0908, which can be approximated as x ≈ 0.091 units per hour.