Operations & Rates
A machine makes candies at a constant rate. In 36 minutes it makes 6 pounds. How many minutes will it take to make 10 pounds?
60 minutes
The ratio of yards to miles is 1,760 : 1.
How many yards are in 3 miles?
5,280 yards
The number 48 is 60% of what number?
80
A basket contains 5 bananas, 7 apples, and 3 oranges. Write the ratio of bananas to oranges in simplest form.
5:3
Ryan drives 10 minutes at 36 miles per hour to reach a customer. How many miles did he drive? (Round to the nearest tenth if needed.)
6.0 miles (36 mph × 10/60 hr = 36 × 1/6 = 6)
Hannah worked 3 hours each night for 8 nights and earned $192 total. What is her hourly rate?
$8 per hour
Convert 5 feet to inches using the ratio 12 inches : 1 foot.
60 inches
12 is what percent of 60?
Express your answer as a percent.
20%
Using the same basket (5 bananas, 7 apples, 3 oranges), write the ratio of total fruit to apples.
15:7
A cyclist travels at 12 miles per hour for 45 minutes. How far does the cyclist travel?
9 miles (12 × 45/60 = 12 × 0.75 = 9)
A baker bakes 15 loaves in 30 minutes at a steady pace. How many loaves does the baker make in 2 hours?
60 loaves
There are 3 feet in a yard. If the ratio of yards to miles is 1,760 : 1, how many feet are in 2 miles?
10,560 feet
A shirt is 25% off its original price of $36. What is the sale price?
$27
Complete the table: If y is directly proportional to x and when x=2, y=10, find y when x=6 and when x=0.5.
When x=6, y=30 (unit rate y/x = 5 → y=5×6=30). When x=0.5, y=2.5.
Jason drives 18 minutes at 48 mph, then 12 minutes at 30 mph. How many total miles did he drive during both segments? Show work.
Jason: 18 min at 48 mph → 48 × 18/60 = 14.4 miles. 12 min at 30 mph → 30 × 12/60 = 6 miles. Total = 20.4 miles.
A printer prints 120 pages in 2 hours. How many pages per minute does the printer produce? Give your answer as a unit rate (pages per minute).
1 page per minute.
A map scale shows 1 inch : 20 miles. If two cities are 85 miles apart, how many inches apart on the map?
4.25 inches
30% of the students in a school are in band. If 210 students are in band, what is the total number of students?
700 students
400 — A table shows earnings for babysitting:
1 hour → $6
3 hours → $18.
Fill in the rows for 4 hours, 8 hours, and 12 hours. Then write the unit rate (dollars per hour).
4 hours → $24; 8 hours → $48; 12 hours → $72. Unit rate $6/hour.
Car A drives at 55 mph for 2 hours and 15 minutes. Car B drives at 60 mph for 1 hour and 45 minutes. How many more miles did Car B travel than Car A?
Car A: 55 × 2.25 = 123.75 miles.
Car B: 60 × 1.75 = 105 miles.
Car A traveled 18.75 more miles.
At a factory, 45 widgets are produced every 9 minutes. If production continues at that rate, how many minutes to produce 300 widgets?
60 minutes
The ratio of minutes to hours is 60 : 1. If a trip lasts 3 hours and 45 minutes, how many minutes long is the trip?
225 minutes
The number 6 is 12% of what number?
50
Two cars have constant speeds.
Car A travels 30 miles in 0.5 hours.
Car B travels 50 miles in 1 hour.
Create a ratio table for distances each car travels in 4 hours, then find the difference in miles traveled after 4 hours.
Car A: 30 mi in 0.5 hr → 60 mph.
In 4 hours: 240 miles.
Car B: 50 mi in 1 hr → 50 mph.
In 4 hours: 200 miles.
Two couriers:
Courier X drives 20 min at 36 mph then 25 min at 42 mph.
Courier Y drives 30 min at 40 mph then 15 min at 50 mph.
During the total driving times, who drove farther and by how many miles? Show work.
Courier X: 20/60 hr at 36 → 36×1/3 = 12. 25/60 hr at 42 → 42×25/60 = 17.5.
Total X = 29.5 miles.
Courier Y: 30/60 hr at 40 → 20. 15/60 hr at 50 → 12.5.
Total Y = 32.5 miles.
Courier Y drove 3.0 miles more.