Lesson 5
Comparing Speeds and Prices
Let’s compare some speeds and some prices.
5.1: Closest Quotient
Is the value of each expression closer to \(\frac12\), 1, or \(1\frac12\)?
- \(20\div 18\)
- \(9\div 20\)
- \(7\div 5\)
5.2: More Treadmills
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 \(\frac12\) hour.
- Mai ran 6.3 kilometers in 45 minutes.
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What is the same about the workouts done by:
- Tyler and Kiran?
- Kiran and Mai?
- Mai and Tyler?
- At what rate did each of them run?
- How far did Mai run in her first 30 minutes on the treadmill?
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 \(\frac12\) hour. Eventually, Kiran ran 1 kilometer more than Tyler. How much time did it take for this to happen?
5.3: The Best Deal on Beans
Four different stores posted ads about special sales on 15-oz cans of baked beans.
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Which store is offering the best deal? Explain your reasoning.
- 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?
Summary
Diego ran 3 kilometers in 20 minutes. Andre ran 2,550 meters in 17 minutes. Who ran faster? Since neither their distances nor their times are the same, we have two possible strategies:
- Find the time each person took to travel the same distance. The person who traveled that distance in less time is faster.
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Find the distance each person traveled in the same time. The person who traveled a longer distance in the same amount of time is faster.
It is often helpful to compare distances traveled in 1 unit of time (1 minute, for example), which means finding the speed such as meters per minute.
Let’s compare Diego and Andre’s speeds in meters per minute.
distance (meters) | time (minutes) |
---|---|
3,000 | 20 |
1,500 | 10 |
150 | 1 |
distance (meters) | time (minutes) |
---|---|
2,550 | 17 |
150 | 1 |
Both Diego and Andre ran 150 meters per minute, so they ran at the same speed.
Finding ratios that tell us how much of quantity \(A\) per 1 unit of quantity \(B\) is an efficient way to compare rates in different situations. Here are some familiar examples:
- Car speeds in miles per hour.
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Fruit and vegetable prices in dollars per pound.
Glossary Entries
- unit price
The unit price is the cost for one item or for one unit of measure. For example, if 10 feet of chain link fencing cost $150, then the unit price is \(150 \div 10\), or $15 per foot.