8th Grade Direct & Inverse Variation Problem Solving

A car travels at a constant speed. If it takes 3 hours to travel 180 miles, how far will it travel in 5 hours at the same speed?

• 240 miles

• 360 miles

• 150 miles

• 300 miles

The cost of apples varies directly with the weight. If 4 pounds of apples cost $8, how much would 10 pounds cost?

• $25

• $20

• $12

• $16

The time it takes to complete a job varies inversely with the number of workers. If 5 workers can complete a job in 12 hours, how long will it take 10 workers to complete the same job?

• 4 hours

• 10 hours

• 8 hours

• 6 hours

A recipe requires 2 cups of flour to make 12 cookies. How many cups of flour are needed to make 30 cookies?

• 3 cups

• 4 cups

• 6 cups

• 5 cups

The intensity of light varies inversely with the square of the distance from the source. If the intensity is 100 units at 2 meters, what is the intensity at 4 meters?

• 50 units

• 10 units

• 75 units

• 25 units

The number of hours a student studies varies directly with their test scores. If a student scores 75 after studying for 3 hours, what score can they expect after studying for 5 hours?

• 90

• 80

• 100

• 125

The speed of a boat varies inversely with the current. If the boat travels at 10 mph in still water, how fast will it go if the current is 2 mph?

• 5 mph

• 8 mph

• 12 mph

• 6 mph

A car's fuel consumption varies inversely with the speed. If a car consumes 30 miles per gallon at 60 mph, how many miles per gallon will it consume at 30 mph?

• 60 miles per gallon

• 75 miles per gallon

• 45 miles per gallon

• 15 miles per gallon

The area of a rectangle varies directly with its length and inversely with its width. If a rectangle has an area of 24 square units with a length of 8 units, what is the width?

• 2 units

• 6 units

• 4 units

• 3 units

The number of pages a printer can print varies inversely with the time taken. If it takes 4 hours to print 200 pages, how long will it take to print 500 pages?

• 5 hours

• 3.2 hours

• 2 hours

• 1.6 hours