What is a Real World Problem For Adding and Subtracting Rational Expressions?

Question

I need help knowing a real world problem for adding and subtracting rational expressions. I need it to connect to my students, so it would be nice if it was something relating to sports or something similar.

Thanks in advance!

Answer 1

Example Adding

John can clean a house by himself in 5 hours. Jacob can clean a house by himself in 7 hours. How long would it take them to clean the house if they worked together?

Define Variables

t = time it takes John and Jacob to clean the house together.

Other Info

1. It takes John 5 hours to clean by himself, in 1 hour he cleans 1/5 of the house & Jacob in 1/7.
2. John and Jacob work together for t hours to clean the house together using,
3. Part of the task completed = rate of work * time spent on the task
4. So we can write that John completed t/5 of the house and Jacob t/7 of the house in this time.

Set up equation.

Since we are trying to find how long it would take for them to clean 1 house together we will have the following equation to find out!

1. t / 5 + t / 7 = 1
2. Solve for t.