Rate Problems
If a car travels 150 miles in 3 hours, what is the rate of speed in miles per hour?
50 miles per hour
Convert the rate of 240 miles in 4 hours to miles per hour.
60 miles per hour
If a bike's price increases from $200 to $250, what is the rate of change in price?
$50 increase
If y varies directly with x and y=8 when x=4, what is the constant of variation?
2
If x/12 = 3/4 what is the value of x?
x= 9
If a factory produces 500 toys in 4 hours, what is the production rate per hour?
125 toys per hour
If 3 gallons of paint cost $54, what is the cost per gallon?
$18 per gallon
A plant grows from 3 inches to 9 inches in 6 weeks. What is the rate of growth per week?
1 inch per week
Write the equation that represents the direct variation if k=3 and y varies directly with x.
y=3x
If 5 yards of fabric cost $45, how much would 8 yards cost?
$72
If a person can read 60 pages in 2 hours, how many pages can they read in 5 hours?
150 pages
A car gets 30 miles per gallon. How many miles can it travel on 15 gallons?
450 miles
If a car's value decreases from $20,000 to $15,000 over 4 years, what is the yearly rate of change?
$1,250 per year
If y=15 when x=5, what is the value of y when x=10?
30
If a recipe requires 2 cups of sugar for every 3 cups of flour, how many cups of sugar are needed for 9 cups of flour?
6 cups
A recipe calls for 2 cups of flour for every 3 cups of sugar. What is the ratio of flour to sugar?
2:3
If you can buy 5 notebooks for $10, what is the price per notebook?
$2 per notebook
A swimmer completes a lap in 30 seconds. If they improve to 25 seconds, what is the rate of change in time?
5 seconds
A table shows that when x=2x=2, y=10y=10 and when x=4x=4, y=20y=20. Is this a direct variation?
Yes, it is a direct variation (constant ratio).
If a car travels 150 miles on 5 gallons of gas, how many gallons will it need to travel 300 miles?
10 gallons
A cyclist travels 36 miles in 2 hours. If they continue at this rate, how far will they travel in 5 hours?
90 miles
A recipe requires 4 tablespoons of sugar for every 2 cups of flour. What is the unit rate of sugar per cup of flour?
2 tablespoons of sugar per cup of flour
If a company’s profits increased from $100,000 to $150,000 over two years, what is the average annual rate of change?
$25,000 average annual increase
If the relationship between x and y is described by the equation y=2x, what is the constant of variation?
2 (the constant of variation is significant as it describes the relationship between xx and y).
If 4 workers can complete a task in 12 hours, how long will it take 6 workers to complete the same task?
8 hours