Table of Contents |
The relationship between work, rate, and time can be modeled using a similar equation to distance, rate, and time:
We multiply the rate at which someone completes work, or a particular job, by the amount of time they spent working.
If two people are working together, we can add their rates together and reflect this in the formula for work, rate, and time.
EXAMPLE
If a professor can grade 10 papers in one hour, and her teaching assistant can grade 7 papers in one hour, we know that their combined rate is 17 papers per hour.In general, if two people are working together, we use as the rate in the formula, to show that Rate 1 and Rate 2 are combined.
Again, to solve a work, rate, time problem in the real world, we'll need to define our variables and create a system of equations.
Let's return to the professor and teaching assistant scenario.
EXAMPLE
A professor can grade 80 papers in the same amount of time it takes for her teaching assistant to grade 60 papers. The teaching assistant grades 1 less paper per hour than the professor. How many papers can the two grade in one hour?Using this equation, substitute for | |
Distribute t | |
From our first equation, substitute 80 for | |
Subtract 80 from both sides | |
Divide both sides by -1 | |
Solve for t |
Using the combined rate equation, substitute 20 in for t | |
Divide both sides by 20 | |
Our Solution |
Now we'll look at an example where we find individual rates per hour.
EXAMPLE
Suppose Kate and Jenny work in a bicycle shop. Jenny can repair 48 bikes in the same amount of time that it takes Kate to repair 32 bikes. Also, Jenny can repair 2 more bikes per hour than Kate can. We want to know the rate per hour that Jenny repairs bikes and the rate per hour that Kate repairs bikes.Using our first equation, substitute for | |
An equivalent equation |
Using the equivalent equation, cross-multiply with the denominators | |
Simplify | |
Distribute | |
Subtract from both sides | |
Divide both sides by 16 | |
Kate's rate is 4 bike per hour |
Using the second equation, substitute 4 in for | |
Add 4 and 2 | |
Jenny's rate is 6 bikes per hour |
Source: ADAPTED FROM "BEGINNING AND INTERMEDIATE ALGEBRA" BY TYLER WALLACE, AN OPEN SOURCE TEXTBOOK AVAILABLE AT www.wallace.ccfaculty.org/book/book.html. License: Creative Commons Attribution 3.0 Unported License