# Illustrative Mathematics Unit 6.3, Lesson 5: Comparing Speeds and Prices

Learning Targets:

• I understand that if two ratios have the same rate per 1, they are equivalent ratios.
• When measurements are expressed in different units, I can decide who is traveling faster or which item is the better deal by comparing “how much for 1” of the same unit.

Related Pages
Illustrative Math

### Lesson 5: Comparing Speeds and Prices

Let’s compare some speeds and some prices.

Illustrative Math Unit 6.3, Lesson 5 (printable worksheets)

### Lesson 5 Summary

The following diagram shows how to use ratios to compare rates.

### Lesson 5.1 Closest Quotient

Is the value of each expression closer to ½, 1, 1½

1. 20 ÷ 18
2. 9 ÷ 20
3. 7 ÷ 5

Scroll down the page for the answer to the question about Tyler and Kiran.

Some students did treadmill workouts, each one running at a constant speed. Answer the questions about their workouts. Explain or show your reasoning.

• Tyler ran 4,200 meters in 30 minutes.
• Kiran ran 6,300 meters in ½ hour.
• Mai ran 6.3 kilometers in 45 minutes.
1. What is the same about the workouts done by:
a. Tyler and Kiran?
b. Kiran and Mai?
c. Mai and Tyler?
2. At what rate did each of them run?
3. How far did Mai run in her first 30 minutes on the treadmill?

#### Are you ready for more?

Tyler and Kiran each started running at a constant speed at the same time. Tyler ran 4,200 meters in 30 minutes and Kiran ran 6,300 meters in ½ hour. Eventually, Kiran ran 1 kilometer more than Tyler. How much time did it take for this to happen?

#### Lesson 5.3 - The Best Deal on Beans

Four different stores posted ads about special sales on 15-oz cans of baked beans.

1. Which store is offering the best deal? Explain your reasoning.Which store is offering the best deal? Explain your reasoning.
2. The last store listed is also selling 28-oz cans of baked beans for \$1.40 each. How does that price compare to the other prices?

#### Lesson 5 Practice Problems

1. Mai and Priya were on scooters. Mai traveled 15 meters in 6 seconds. Priya travels 22 meters in 10 seconds. Who was moving faster? Explain your reasoning.
2. Here are the prices for cans of juice that are the same brand and the same size at different stores. Which store offers the best deal? Explain your reasoning.
Store X: 4 cans for \$2.48
Store Y: 5 cans for \$3.00
Store Z: 59 cents per can
3. Costs of homes can be very different in different parts of the United States.
a. A 450-square-foot apartment in New York City costs \$540,000. What is the price per square foot? Explain or show your reasoning.
b. A 2,100-square-foot home in Cheyenne, Wyoming, costs \$110 per square foot. How much does this home cost? Explain or show your reasoning.
4. There are 33.8 fluid ounces in a liter. There are 128 fluid ounces in a gallon. About how many liters are in a gallon?
a. 2
b. 3
c. 4
d. 5
Is your estimate larger or smaller than the actual number of liters in a gallon? Explain how you know.
5. Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? Explain your reasoning.
6. Name an object that could be about the same length as each measurement. a. 4 inches b. 6 feet c. 1 meter d. 5 yards e. 6 centimeters f. 2 millimeters g. 3 kilometers

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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