Rate Problems

Unit Rates

A rate compares two quantities with different units.

A unit rate is a rate in which the second number is 1.

48 miles in 8 hours

6 gallons per minute

$0.60 for 1 apple

$12.50 for 1 T-shirt

42 miles per gallon

$70 for 5 DVDs

$3.60 for 12 oranges

Which rates are unit rates?

Find Unit Rates

Divide the first term in the rate by the second term.

When the second term is 1 unit, it becomes the unit rate.

Find the unit rate or unit price.

Emma hiked 9 miles in 4 hours.

What is her rate of speed?

9 ÷ 4 = 2.25

The unit rate (rate of speed)is 2.25 miles per hour.

A store charges $5.70 for15 ounces of oregano.

What is the unit price?

5.70 ÷ 15 = 0.38

The unit price is $0.38 per ounce.

810 miles in 15 hours

$504 for 32 cases of juice drinks

Find Unit Rates

Divide the first term in the rate by the second term.

When the second term is 1 unit, it becomes the unit rate.

Find the unit rate or unit price.

Emma hiked 9 miles in 4 hours.

What is her rate of speed?

9 ÷ 4 = 2.25

The unit rate (rate of speed)is 2.25 miles per hour.

A store charges $5.70 for15 ounces of oregano.

What is the unit price?

5.70 ÷ 15 = 0.38

The unit price is $0.38 per ounce.

810 miles in 15 hours 54 miles per hour

$504 for 32 cases of juice drinks $15.75 per case

Rate Problems Involving Distance, Rate, and Time

Use this formula to solve rate problems involving distance, rate, and time:

Maya rode 18 miles on her bicycle at an average rate of 5 miles per hour.

How long did it take Mayato ride 18 miles?

d = rt

d = distance r = rate t = time

Hayden drove 468 miles to Flagstaff in 9 hours. What was

his average rate of speed?

Kelley averaged 3.5 miles per hour on a mountain hike. She hiked for 8

hours. How many miles did she hike?

Solve the rate problems.

d = rt18 = 5t

It took Maya 3.6 hours to ride 18 miles.

3.6 = t

18 5t

5 5 =

Rate Problems Involving Distance, Rate, and Time

Use this formula to solve rate problems involving distance, rate, and time:

Maya rode 18 miles on her bicycle at an average rate of 5 miles per hour.

How long did it take Mayato ride 18 miles?

d = rt

d = distance r = rate t = time

Hayden drove 468 miles to Flagstaff in 9 hours. What was

his average rate of speed?

52 miles per hour

Kelley averaged 3.5 miles per hour on a mountain hike. She hiked for 8

hours. How many miles did she hike?

28 miles

Solve the rate problems.

d = rt18 = 5t

It took Maya 3.6 hours to ride 18 miles.

3.6 = t

18 5t

5 5 =

Rate Problems Involving Simple Interest

Use this formula to solve problems involving simple interest: I = prtI = Interest (amount of money earned)p = Principal (initial amount of money)r = Rate (usually given as a percent; convert to decimal form)t = Time (if less than a year, convert to decimal form)

Conrad deposited $1,250 in a bank account that earns 4% simple interest. How much

will be in his account after 6 months?

I = prt

I = 1,250 × 0.04 × 0.5

4% = 0.04; 6 months = 0.5 year

I = 25

$1,250 + $25 = $1275

Conrad will have $1275 in hisaccount after 6 months.

Solve the simpleinterest problem.

Kayla paid $3,360 in interest on a car loan. She paid 8%

interest for 3 years.

What was the price of the car?

Rate Problems Involving Simple Interest

Use this formula to solve problems involving simple interest: I = prtI = Interest (amount of money earned)p = Principal (initial amount of money)r = Rate (usually given as a percent; convert to decimal form)t = Time (if less than a year, convert to decimal form)

Conrad deposited $1,250 in a bank account that earns 4% simple interest. How much

will be in his account after 6 months?

I = prt

I = 1,250 × 0.04 × 0.5

4% = 0.04; 6 months = 0.5 year

I = 25

$1,250 + $25 = $1275

Conrad will have $1275 in hisaccount after 6 months.

Solve the simpleinterest problem.

Kayla paid $3,360 in interest on a car loan. She paid 8%

interest for 3 years.

What was the price of the car?

$14,000

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