unit rates
DESCRIPTION
Solving rates in AlgeTRANSCRIPT
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Unit Rates
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Vocabulary
• A rate is a ratio that compares two quantities measured in different units.
• The unit rate is the rate for one unit of a given quantity. Unit rates have a denominator of 1.
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ExamplesRate: 150 heartbeats
2 minutes
Unit Rate (Divide to get it):
150 ÷ 2 = 75 heartbeats per minute.
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Find the Unit RateAmy can read 88 pages in 4 hours. What is the unit rate? (How many pages can she read per hour?)
88 pages4 hours
22 pages / hour
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Using Unit Rates
• You can find the missing terms of equal ratios.
• Use the unit rate, and set it equal to another ratio.
• Solve for what is missing by dividing or multiplying.
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ExampleJoe’s car goes 25 miles per gallon of gasoline. How far can it go on 8 gallons of gasoline?
25 miles1 gallonUnit
Rate
=8 gallons
x 8
x 8
25 x 8 = 200. Joe’s car can go 200 miles on 8 gallons of gas.
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Comparing Unit Prices
• Use division to find the unit prices of the two products in question.
• The unit rate that is smaller (costs less) is the better value.
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Example
Juice is sold in two different sizes. A 48-fluid ounce bottle costs $2.07. A 32-fluid ounce bottle costs $1.64. Which is the better buy?
$2.0748 fl.oz. $0.04 per fl.oz.
$1.6432 fl.oz.
$0.05 per fl.oz.
The 48 fl.oz. bottle is the better value.
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Marge can clean the house in 3 hrs. Lisa can clean it in 5 hrs.
How long will it take them to clean the house if they both work together?
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Marge can clean the house in 3 hrs.,
so she does 1/3 of the house per hour.
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Lisa can clean the house in 5 hrs.,
so she does 1/5 of the house per hour.
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Let T T be the time in hours.
13 TT + 1
5 TT = 1
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1/3T + 1/5T = 1
15(1/3T + 1/5T) = 15(1)
5T + 3T = 15
8T = 15
T = 15/8
17/8 hrs.
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Bart can wash the car in 20 min.Homer can wash it in 30 min.How long will it take them to wash the car if they both work together?
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Bart can wash the car in 20 min.,
so he does 1/20 of the car per min.
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Homer can wash the car in 30 min.,
so he does 1/30 of the car per min.
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Let M M be the time in minutes.
120 MM + 1
30 MM = 1
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1/20M + 1/30M = 1
60(1/20M + 1/30M) = 60(1)
3M + 2M = 60
5M = 60
M = 12 min.
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Mr. Skinner can enroll 15 students per hr.
Mr. Chalmer can enroll 20 students per hr.
How long will it take them to enroll 140 students working together?
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Minutes work better than hours.
Mr. Skinner enrolls 15 students per 60 min.,
so he enrolls 15/60 or 1/4 students per min.
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Minutes work better than hours.
Mr. Chalmer enrolls 20 students per 60 min.,
so he enrolls 20/60 or 1/3 students per min.
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1/4M + 1/3M = 140
12(1/4M + 1/3M) = 12(140)
3M + 4M = 1680
7M = 1680M = 240 min.
= 4 hrs.
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Mrs. Krabappel can grade a set of papers in 11/2 hrs.
Miss Hoover can grade them in 80 min.
How long will it take them to grade one set if they both work together?
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Minutes work better than hours.
Mrs. Krabappel grades 1/90 of a set per min.
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Miss Hoover grades 1/80 of a set per min.
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1/90M + 1/80M = 1
720(1/90M + 1/80M) = 720(1)
8M + 9M = 720
17M = 720
M = 426/17 min.
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Approximately how long would it take them to grade 3 sets if they both work together?
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1/90M + 1/80M = 3
720(1/90M + 1/80M) = 720(3)
8M + 9M = 2160
17M = 2160
M = 1271/17 min. A little more than 2 hrs.
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