Unit Rates are Unit Great!

Using Unit Rates

100

A car travels 180 miles in 6 hours. What is the car's speed in miles per hour (unit rate)?

If the car continues at the same speed, how far will it travel in 10 hours?

The speed is 180 miles ÷ 6 = 30 miles per hour.

In 10 hours, the car will travel 30 miles×10 hours = 300 miles

200

Sarah buys 4 apples for $2. What is the cost of 1 apple?

Once you find the cost of 1 apple, how much would 10 apples cost?

The cost of 1 apple is $2 ÷ 4 = $0.50

 
10 apples would cost 10 × 0.50= $5.00

300

Ms Sutherland buys 3 oz of ice cream for $3.60, how much would 8 oz cost?

Dollars per oz = $3.60 ÷ 3 = $1.20 each

$1.20 x 8 oz = $9.60

Solving Rate Problems

100

A factory produces 120 toys in 4 hours. What is the rate of production in toys per hour?

Answer: The rate is 120 ÷ 4 = 30 toys per hour.

200

10 cm equals about 4 inches.

How many cm per inch?

How many inches per cm?

10cm / 4 = 2.5 cm per inch

4 inch/ 10 = 0.4 inches per cm

300

Two trains start from different stations and are heading toward each other. Train A is traveling at 60 miles per hour, and Train B is traveling at 40 miles per hour. The distance between the two stations is 200 miles.

Question 1:
How fast are the two trains closing the gap between each other?

Question 2:
How long will it take for the two trains to meet?

To find how fast the trains are closing the gap, you simply add their speeds together:

• Train A is going 60 miles per hour, and Train B is going 40 miles per hour.
• Total speed = 60+40=10060 + 40 = 10060+40=100 miles per hour.

The trains are closing the gap at 100 miles per hour.

Question 2:Since they close the gap at 100 miles each hour it will take 2 hours to meet from 200 miles apart.

Better/Faster/Stronger

100

Two brands of cereal are on sale at the store.

• Brand A costs $6 for a 12-ounce box.
• Brand B costs $8 for a 16-ounce box.

Question:
Which brand of cereal is the better deal?

They are both equivalent because they both have the same unit rate!

Brand A: $6 / 12 = $0.50/oz

Brand B: $8 / 16 = $0.50/oz

200

Two cars have different gas mileage:

• Car A gets 300 miles on 10 gallons of gas.
• Car B gets 375 miles on 12 gallons of gas.

Question:
Which car gets better gas mileage (miles per gallon)?

Car B gets better gas mileage, with 31.25 miles per gallon, compared to Car A's 30 miles per gallon.

300

Two runners are racing on a track. Runner A runs 5 miles in 40 minutes, while Runner B runs 6 miles in 50 minutes.

Question:
Which runner is faster?

Solution:

• Runner A: Speed = 5 miles/40 = 0.125 miles per minute.
• Runner B: Speed = 6 miles/50 = 0.12 miles per minute.