Mastering Direct & Inverse Variation: Grade 8 Challenge

1. A car travels at a constant speed. If it takes 4 hours to travel 240 miles, how does the time taken vary with the distance traveled? Identify the type of variation.

• The time taken varies inversely with the distance traveled.

• The time taken varies exponentially with the distance traveled.

• The time taken varies directly with the distance traveled.

• The time taken is constant regardless of the distance traveled.

2. The cost of apples varies directly with the weight. If 3 pounds of apples cost $6, how much would 5 pounds cost?

• $12

• $8

• $10

• $15

3. The number of workers needed to complete a task varies inversely with the time taken. If 4 workers can finish a job in 10 hours, how long would it take 8 workers to finish the same job?

• 4 hours

• 6 hours

• 5 hours

• 8 hours

4. A recipe requires sugar and flour in a direct variation. If 2 cups of sugar are needed for 5 cups of flour, how many cups of sugar are needed for 15 cups of flour?

• 4 cups of sugar

• 8 cups of sugar

• 6 cups of sugar

• 10 cups of sugar

5. The speed of a boat varies inversely with the time it takes to travel a fixed distance. If it takes 3 hours to travel 60 miles, how long will it take if the speed is doubled?

• 1.5 hours

• 2 hours

• 6 hours

• 4 hours

6. The amount of gas consumed by a car varies directly with the distance traveled. If a car uses 10 gallons for 200 miles, how many gallons will it use for 500 miles?

• 25 gallons

• 15 gallons

• 30 gallons

• 20 gallons

7. The brightness of a light bulb varies inversely with the distance from the bulb. If a bulb is 2 feet away and has a brightness of 100 lumens, what will be the brightness at 4 feet?

• 50 lumens

• 200 lumens

• 75 lumens

• 25 lumens

8. The number of pages printed varies directly with the time spent printing. If 50 pages are printed in 2 minutes, how many pages can be printed in 5 minutes?

• 125 pages

• 150 pages

• 100 pages

• 75 pages

9. The time taken to complete a project varies inversely with the number of people working on it. If 6 people can complete it in 12 days, how long will it take 3 people?

• 18 days

• 30 days

• 36 days

• 24 days

10. The price of a concert ticket varies directly with the number of tickets sold. If 100 tickets are sold for $20 each, what will be the price per ticket if 200 tickets are sold?

• $15

• $10

• $25

• $5