Proportional Reasoning with Rates — Practice
A rate compares two different kinds of quantity. Turn it into a unit rate and you can compare anything.
What these questions cover
These questions use 1 idea from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Better buy — The option with the lower unit price.
Problem 1
A car travels 250 miles in 5 hours. Find the speed in miles per hour.
Worked answer
50
250 ÷ 5 = 50
The car covers 50 miles every hour.
Problem 2
Six pounds of apples cost $12.60. What is the cost per pound?
Worked answer
2.10
12.60 ÷ 6 = 2.10
Each pound costs $2.10.
Problem 3
Leo types 480 words in 8 minutes. How many words per minute?
Worked answer
60
480 ÷ 8 = 60
60 words each minute.
Problem 4
Five notebooks cost $7.25. What does one notebook cost?
Worked answer
1.45
7.25 ÷ 5 = 1.45
One notebook costs $1.45.
Problem 5
A car drives 360 miles using 12 gallons of gas. Find the miles per gallon.
Worked answer
30
360 ÷ 12 = 30
30 miles for each gallon.
Problem 6
A 15-ounce jar costs $4.35. A 24-ounce jar costs $6.72. Which is the better buy?
- The 15-ounce jar
- The 24-ounce jar
- They cost the same per ounce
Worked answer
The 24-ounce jar
15-ounce: 4.35 ÷ 15 = 0.29 per ounce
24-ounce: 6.72 ÷ 24 = 0.28 per ounce
0.28 < 0.29, so the larger jar is cheaper per ounce.
Problem 7
A snail crawls 34 mile in 12 hour. What is its speed in miles per hour?
Worked answer
1.5
34 ÷ 12 = 34 × 21
= 64 = 32 = 1.5
In a full hour it travels 1.5 miles.
Problem 8
Nina paints 23 of a room in 35 of an hour. How many rooms per hour?
Worked answer
10/9
23 ÷ 35 = 23 × 53
= 109
A little more than one room per hour.
Problem 9
A printer runs at 22 pages per minute. How many minutes to print 341 pages?
Worked answer
15.5
341 ÷ 22 = 15.5
It takes 15.5 minutes.
Problem 10
A recipe uses 34 cup of sugar for 2 dozen cookies. How much sugar per dozen?
Worked answer
3/8
34 ÷ 2 = 34 × 12
= 38 cup per dozen.
Problem 11
A heart beats 72 times a minute. How many beats in 1 hour and 30 minutes?
Worked answer
6480
1 hr 30 min = 90 minutes
72 × 90 = 6480 beats
Problem 12
A car travels at 45 miles per hour. How far does it go in 2 hours and 20 minutes?
Worked answer
105
Time = 213 = 73 hours
45 × 73 = 15 × 7 = 105 miles
Problem 13
A faucet fills 58 of a tank in 15 minutes. How many minutes to fill the whole tank?
Worked answer
24
One eighth takes 15 ÷ 5 = 3 minutes
Eight eighths take 3 × 8 = 24 minutes
Or: 15 ÷ 58 = 15 × 85 = 24.
Problem 14
A shop sells pens 3 for $4.80 or 5 for $7.75. How many cents cheaper per pen is the better deal?
Worked answer
5
4.80 ÷ 3 = $1.60 each
7.75 ÷ 5 = $1.55 each
1.60 - 1.55 = $0.05, which is 5 cents.
Problem 15
Kai drives 60 miles at 30 mph, then 60 miles at 60 mph. What is his average speed for the whole trip?
Worked answer
40
First leg: 60 ÷ 30 = 2 hours
Second leg: 60 ÷ 60 = 1 hour
Total: 120 miles in 3 hours
120 ÷ 3 = 40 mph — less than 45, because he spent longer going slowly.
Problem 16
A machine makes 7 parts every 4 minutes. How many parts in 3 hours?
Worked answer
315
3 hours = 180 minutes
180 ÷ 4 = 45 blocks
45 × 7 = 315 parts