Unit Rates

Show your work for each problem.

1.
A pack of 6 juice boxes costs 9 dollars. What is the unit rate?
1. a)54 dollars per box
2. b)0.67 dollars per box
3. c)1.50 dollars per box
4. d)6 dollars per box
Answer: 1.50 dollars per box
. The unit rate is 1.50 dollars per box. The wrong answer 0.67 comes from dividing boxes by price (6/9), and 54 comes from multiplying instead of dividing.
2.
A car travels 180 kilometers in 3 hours. What is its speed in km/h?
Answer: 60
Speed is a unit rate. km/h.
3.
Which is a unit rate?
1. a)15 pages in 3 days
2. b)120 km in 2 hours
3. c)45 km per hour
4. d)8 apples for 4 dollars
Answer: 45 km per hour
45 km per hour has '1 hour' as the second quantity. The others compare to 2, 4, or 3 units - they are rates but not unit rates.
4.
A printer prints 120 pages in 4 minutes. How many pages does it print per minute?
Answer: 30
pages per minute.
5.
A store sells 4 notebooks for 10 dollars. What is the price per notebook?
Answer: 2.50
1. What is the total price? 10
2. How many notebooks are there? 4
3. What is 10 divided by 4? 2.50
6.
Store A sells 3 pens for 6 dollars. Store B sells 5 pens for 9 dollars. Which store has the better price per pen?
1. a)Store A (2 dollars/pen)
2. b)Store B (1.80 dollars/pen)
3. c)Both are equal
4. d)Cannot be determined
Answer: Store B (1.80 dollars/pen)
Store A: dollars/pen. Store B: dollars/pen. Store B has the lower unit rate, so it's the better deal.
7.
A cyclist travels at 24 km/h. How many kilometers will they travel in 2.5 hours?
Answer: 60
Using the unit rate: kilometers.
8.
A factory produces 450 items in 6 hours. How many items will it produce in 10 hours?
Answer: 750
1. What is the production rate per hour? (450 / 6) 75
2. How many hours do we want to calculate for? 10
3. What is 75 items/hour times 10 hours? 750
9.
A 500ml bottle costs 2 dollars. A 750ml bottle costs 2.70 dollars. Which has the better unit price per liter?
1. a)Both are equal
2. b)750ml bottle (3.60 dollars/L) - this is correct
3. c)750ml bottle (3.60 dollars/L)
4. d)500ml bottle (4 dollars/L)
Answer: 750ml bottle (3.60 dollars/L)
500ml bottle: dollars/L. 750ml bottle: dollars/L. The 750ml bottle is better value.
10.
A train travels 280 km in 4 hours. How long will it take to travel 420 km at the same speed?
Answer: 6
Speed: km/h. Time for 420 km: hours.
11.
Maria types 180 words in 4 minutes. How many words can she type in 15 minutes?
Answer: 675
1. How many words does Maria type per minute? (180 / 4) 45
2. What is 45 words/minute times 15 minutes? 675
12.
Car A uses 32 liters of fuel to travel 400 km. Car B uses 45 liters to travel 600 km. Which car is more fuel-efficient?
1. a)Car B (7.5 L/100km)
2. b)Car A (12.5 km/L)
3. c)Both are equal
4. d)Car A (8 L/100km)
Answer: Car B (7.5 L/100km)
Car A: L/100km. Car B: L/100km. Car B uses less fuel per 100 km, so it's more efficient.
13.
A machine produces 840 parts in 7 hours. Another machine produces 1020 parts in 9 hours. How many more parts per hour does the faster machine produce?
Answer: 7
Machine 1: parts/h. Machine 2: parts/h. Difference: parts/h more for Machine 1.
14.
A phone plan charges 45 dollars for 10 GB of data. Another plan charges 60 dollars for 15 GB. How much cheaper per GB is the better plan?
Answer: 0.50
1. What is the price per GB for the first plan? (45 / 10) 4.50
2. What is the price per GB for the second plan? (60 / 15) 4
3. Which plan is cheaper per GB? second
4. How much cheaper is it? (4.50 - 4) 0.50
15.
Worker A earns 96 dollars for 8 hours of work. Worker B earns 130 dollars for 10 hours. If they both work 40 hours, how much more will Worker B earn?
Answer: 40
Worker A: dollars/h. For 40h: dollars. Worker B: dollars/h. For 40h: dollars. Difference: dollars.
16.
A recipe calls for 3 cups of flour for every 2 cups of sugar. If you have 9 cups of flour, how many cups of sugar do you need?
Answer: 6
1. What is the ratio of sugar to flour? (2 sugar per 3 flour) 2/3
2. How many cups of flour do you have? 9
3. What is 9 times 2/3? 6