MCR Chapter 6.8 * Direct and Inverse Variation
* Use the Pdf textbook pages 390 - 393 for examples in setting up these questions.
* When you're finished, take a picture of you work and email it to me.
* Show your work/calculations/formulas used.
* Put a box around your answers so they're easy to identify.
1. The distance, d, a car travels is directly proportional to the speed, s, the car is traveling.
Determine the distance traveled if the constant of proportionality, k, is 2 and the speed is 55 mph.
2. The amount of tuition a part-time college student is billed, A, varies directly as the number of credits, C, the student is
taking. If a student is billed $1,520 for 8 credits, how much would a student be billed for taking 10 credits?
3. The income, I, for a kiddie train at an amusement park is directly proportional to the number of tickets sold, n.
If the income, I, is $33 when 22 tickets are sold, determine the income when 38 tickets are sold.
4. The horsepower it takes to propel a speedboat, P, is directly proportional to the square of the velocity, v, of the boat.
If it takes 900 horsepower for the boat to travel at 45 mph, what horsepower is needed to propel the speedboat at 54 mph?
5. The area of a circle, A, is directly proportional to the square of the radius of a circle, r.
If the area of a circle is about 78.5 square inches when the radius is 5 in, determine the area when the radius is 12 in.
6. The time, t, it takes to nail in shingles on a roof is inversely proportional to the number of people nailing in the shingles, n. When three people are nailing in the shingles it takes 7 hours to complete the job. How long will it take to complete the job if five people are nailing in the shingles?
7. The receipts, r, at an international league baseball park are directly proportional to the number of people attending the game, n. If the receipts for a game are $37,200 when 1200 people attend, determine how many people attend if the receipts for a game are $31,000.
8. The time, t, it takes to clean all the windows in a large office building is inversely proportional to the number of teams, n, of window workers used. If six teams can clean all the windows in 20 days, how many teams are used if the windows are cleaned in 12 days?
9. The velocity, v, of a falling object is directly proportional to the square of the time, t, it has been in free fall. An object has been in free fall for 2 seconds has a velocity of 64 feet per second. Determine the velocity of an object that has been falling for 8 seconds.
10. For a cylinder of a specific volume, the height, h, of the cylinder is inversely proportional to the square of the radius of the cylinder, r. When the radius is 6 inches, the height is 10 inches. Determine the height when the radius is 5 inches.
* Use the Pdf textbook pages 390 - 393 for examples in setting up these questions.
* When you're finished, take a picture of you work and email it to me.
* Show your work/calculations/formulas used.
* Put a box around your answers so they're easy to identify.
1. The distance, d, a car travels is directly proportional to the speed, s, the car is traveling.
Determine the distance traveled if the constant of proportionality, k, is 2 and the speed is 55 mph.
2. The amount of tuition a part-time college student is billed, A, varies directly as the number of credits, C, the student is
taking. If a student is billed $1,520 for 8 credits, how much would a student be billed for taking 10 credits?
3. The income, I, for a kiddie train at an amusement park is directly proportional to the number of tickets sold, n.
If the income, I, is $33 when 22 tickets are sold, determine the income when 38 tickets are sold.
4. The horsepower it takes to propel a speedboat, P, is directly proportional to the square of the velocity, v, of the boat.
If it takes 900 horsepower for the boat to travel at 45 mph, what horsepower is needed to propel the speedboat at 54 mph?
5. The area of a circle, A, is directly proportional to the square of the radius of a circle, r.
If the area of a circle is about 78.5 square inches when the radius is 5 in, determine the area when the radius is 12 in.
6. The time, t, it takes to nail in shingles on a roof is inversely proportional to the number of people nailing in the shingles, n. When three people are nailing in the shingles it takes 7 hours to complete the job. How long will it take to complete the job if five people are nailing in the shingles?
7. The receipts, r, at an international league baseball park are directly proportional to the number of people attending the game, n. If the receipts for a game are $37,200 when 1200 people attend, determine how many people attend if the receipts for a game are $31,000.
8. The time, t, it takes to clean all the windows in a large office building is inversely proportional to the number of teams, n, of window workers used. If six teams can clean all the windows in 20 days, how many teams are used if the windows are cleaned in 12 days?
9. The velocity, v, of a falling object is directly proportional to the square of the time, t, it has been in free fall. An object has been in free fall for 2 seconds has a velocity of 64 feet per second. Determine the velocity of an object that has been falling for 8 seconds.
10. For a cylinder of a specific volume, the height, h, of the cylinder is inversely proportional to the square of the radius of the cylinder, r. When the radius is 6 inches, the height is 10 inches. Determine the height when the radius is 5 inches.