Understanding Rates
What is a rate?
A rate is a ratio that compares two quantities with different units (e.g., miles per hour).
What is the rate if someone travels 30 miles in one hour?
30 miles/hour
If a car travels 150 miles in 3 hours, what is the rate?
50 miles/hour (since 150 div3=50)
Which is a better deal: 5 pounds of apples for $10 or 3 pounds for $6?
5 pounds for $10 is $2 per pound;
3 pounds for $6 is $2 per pound.
They are equivalent.
How is a rate different from a ratio?
A rate compares different units (e.g., speed), while a ratio compares similar units (e.g., 2:3).
What is the rate of a person who completes 4 tasks in 2 hours?
2 tasks/hour (since 4 div2=2)
A runner completes 5 laps in 20 minutes. What is the rate in laps per minute?
0.25 laps/minute (since 5 div20=0.25)
If Car A travels 300 miles in 5 hours and Car B travels 400 miles in 6 hours, which car has a higher rate?
Car A: 60 miles/hour (300 div5);
Car B: 66.67 miles/hour (400 div6).
Car B is faster.
If you travel 60 miles in 1 hour, what is your rate of speed?
60 miles/hour
Create a table showing the relationship between hours worked and money earned if someone earns $15 per hour.
Hours Worked-----$
1-----------------$15
3-----------------$30
4----------------$45
5----------------$60
Calculate the rate of water flow if 12 liters are used in 4 hours.
3 liters/hour (since 12 div4=3)
Compare the rates of two workers: Worker A completes 10 tasks in 4 hours, while Worker B completes 8 tasks in 2 hours. Who is more efficient?
Worker A: 2.5 tasks/hour (10 div4);
Worker B: 4 tasks/hour (8 div2).
Worker B is more efficient.
If a car uses 5 gallons of gas to travel 100 miles, what is the rate of miles per gallon?
20 miles/gallon (since 100 div5=20)
If a recipe calls for 3 cups of flour for 4 servings, how many cups are needed for 10 servings? Show your table.
For 4 servings: 3 cups
For 10 servings: 3/4 times10=7.5 cups
If a person reads 120 pages in 2 hours, what is the rate of pages read per hour?
60 tpages/hour (since 120 div2=60)
If one recipe takes 30 minutes to serve 4 and another takes 45 minutes for 6, which one is faster in terms of serving time per person?
Recipe A: 7.5 minutes per person;
Recipe B: 7.5 minutes per person.
They are equivalent.
Define unit rate and give an example
A unit rate is a rate that has a denominator of 1 (e.g., 30 miles per hour)
Construct a rate table for a bike that travels 10 miles per hour for different time intervals (1, 2, 3 hours).
Miles------Hour
10---------1
20---------2
30---------3
How many miles can you travel in 5 hours if your rate is 60 miles per hour?
300 miles (since 60 times5=300)
A train travels 120 miles in 2 hours, while a bus travels 90 miles in 1.5 hours. Which mode of transport is faster?
Train: 60 miles/hour (120 div2);
Bus: 60 miles/hour (90 div1.5).
They are equivalent.