Final answer:
To find how long it would take Nina and Bethany to proof a chapter together, we can set up a system of equations based on their work rates.
Step-by-step explanation:
To find how long it would take Nina and Bethany to work together, we can use the concept of work rate. Let's denote Nina's work rate as x chapters per hour and Bethany's work rate as y chapters per hour. We know that it takes Nina 2 hours (2x chapters) to proof a chapter and Bethany 9 hours (9y chapters) to proof a chapter. When they work together, their combined work rate is the sum of their work rates, so it is (x + y) chapters per hour. To find how long it would take them to proof a chapter together, we can set up the following equation:
2x + 9y = 1 chapter
Let's say it takes them two hours to proof a chapter together. Then their combined work rate is 1/t chapters per hour. We can set up the following equation:
x + y = 1/t
Now we have a system of two equations with two variables. We can solve this system to find the values of x and y, and then calculate t.