# Rational Expressions and Equations

## Solve Uniform Motion and Work Applications



### Solve Uniform Motion Applications

We have solved uniform motion problems using the formula  in previous chapters. We used a table like the one below to organize the information and lead us to the equation.
The formula  assumes we know r and t and use them to find D. If we know D and r and need to find t, we would solve the equation for t and get the formula .
We have also explained how flying with or against a current affects the speed of a vehicle. We will revisit that idea in the next example.
In the next example, we will know the total time resulting from travelling different distances at different speeds.
Once again, we will use the uniform motion formula solved for the variable t.

### Solve Work Applications

Suppose Pete can paint a room in 10 hours. If he works at a steady pace, in 1 hour he would paint  of the room. If Alicia would take 8 hours to paint the same room, then in 1 hour she would paint  of the room. How long would it take Pete and Alicia to paint the room if they worked together (and didn’t interfere with each other’s progress)?
This is a typical ‘work’ application. There are three quantities involved here – the time it would take each of the two people to do the job alone and the time it would take for them to do the job together.
Let’s get back to Pete and Alicia painting the room. We will let t be the number of hours it would take them to paint the room together. So in 1 hour working together they have completed  of the job.
In one hour Pete did  of the job. Alicia did  of the job. And together they did  of the job.
We can model this with the word equation and then translate to a rational equation. To find the time it would take them if they worked together, we solve for t.


Keep in mind, it should take less time for two people to complete a job working together than for either person to do it alone.

### Practice Makes Perfect

Solve Uniform Motion Applications
In the following exercises, solve uniform motion applications
Solve Work Applications
In the following exercises, solve work applications.

### Everyday Math


### Writing Exercises


### Self Check

ⓐ After completing the exercises, use this checklist to evaluate your mastery of the objectives of this section.
ⓑ On a scale of 1–10, how would you rate your mastery of this section in light of your responses on the checklist? How can you improve this?