# Solve Problems with Unit Rates

Videos and solutions to help Grade 6 students learn how to solve problems by analyzing different unit rates.

### New York State Common Core Math Grade 6, Module 1,Lesson 19

Lesson 19 Student Outcomes

• Students solve problems by analyzing different unit rates given in tables, equations, and graphs.

Lesson 19 Summary

• When comparing rates and ratios, it is best to find the unit rate.
• Comparing unit rates can happen across tables, graphs, and equations.

NYS Math Module 1 Grade 6 Lesson 19 Classwork
Analyze tables, graphs, and equations in order to compare rates.

Examples 1–2: Creating Tables from Equations
1. The ratio of cups of blue paint to cups of red paint is 1:2, which means for every cup of blue paint, there are two cups of red paint. In this case, the equation would be red = 2 x blue or r = 2b, where b represents the amount of blue paint and r represents the amount of red paint. Make a table of values.

2. Ms. Siple is a librarian who really enjoys reading. She can read 3/4 of a book in one day. This relationship can be represented by the equation days = 3/4 books, which can be written as d = 3/4 b, where b is the number of books and d is the number of days.

Exercises
1. Bryan and ShaNiece are both training for a bike race and want to compare who rides his or her bike at a faster rate. Both bikers use apps on their phones to record the time and distance of their bike rides. Bryan’s app keeps track of his route on a table, and ShaNiece’s app presents the information on a graph. The information is shown below.
a. At what rate does each biker travel? Explain how you arrived at your answer.
b. ShaNiece wants to win the bike race. Make a new graph to show the speed ShaNiece would have to ride her bike in order to beat Bryan.

2. Braylen and Tyce both work at a movie store and are paid by the hour. The manager told the boys they both earn the same amount of money per hour, but Braylen and Tyce did not agree. They each kept track of how much money they earned in order to determine if the manager was correct. Their data is shown below.
Braylen: m = 10.50h where h is the number of hours worked and m is the amount of money Braylen was paid
Tyce: ____
a. How much did each person earn in one hour?
b. Was the manager correct? Why or why not?

3. Claire and Kate are entering a cup stacking contest. Both girls have the same strategy: stack the cups at a constant rate so that they do not slow down at the end of the race. While practicing, they keep track of their progress, which is shown below.
a. At what rate does each girl stack her cups during the practice sessions?
b. Kate notices that she is not stacking her cups fast enough. What would Kate’s equation look like if she wanted to stack cups faster than Claire?

NYS Math Module 1 Grade 6 Lesson 19 Problem Set
1. Victor was having a hard time deciding on which new vehicle he should buy. He decided to make the final decision based on the gas efficiency of each car. A car that is more gas efficient gets more miles per gallon of gas. When he asked the manager at each car dealership for the gas mileage data, he received two different representations, which are shown below.
a. If Victor based his decision only on gas efficiency, which car should he buy? Provide support for your answer.
b. After comparing the Legend and the Supreme, Victor saw an advertisement for a third vehicle, the Lunar. The manager said that the Lunar can travel about 289 miles on a tank of gas. If the gas tank can hold 17 gallons of gas, is the Lunar Victor’s best option? Why or why not? Word Problems
Peter was having a hard time deciding on which new vehicle he should buy. He decided to make the final decision based on the gas efficiency of each car. A car that is more gas efficient gets more miles per gallon of gas. When he asked the manager at each car dealership for the gas mileage data, he received two different representations, which are shown below.
a. If Peter based his decision only on gas efficiency, which car should he buy? Provide support for your answer.
b. After comparing the Ford and the Honda, Peter saw an advertisement for a third vehicle, the Toyota. The manager said that the Toyota can travel about 238 miles on a tank of gas. If the gas tank can hold 17 gallons of gas, is the Toyota Peter’s best option? Why or why not?

Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.