Question

It takes Nina 2 hours to proof a chapter of Hawkes Learning Systems' Intermediate Algebra book and it takes Bethany 9 hours. How long would it take them working together?

Answer 1

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.