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Variations #2

1. The time it takes you to get to campus varies inversely as your driving speed. Averaging 20 miles per hour in bad traffic, it takes you 1.5 hours to get to campus. How long would the trip take averaging 50 miles per hour?

2. A person’s weekly pay is directly proportional to the number of hours worked. Shawn’s pay is $123.00 for 20 hours of work. Find the amount of pay for 31 hours of work.

3. Kinetic energy varies jointly as the mass and the square of the velocity. A mass of 8 grams and a velocity of 5 centimeters per second has a kinetic energy of 100 ergs. Find the kinetic energy for a mass of 6 grams and a velocity of 9 centimeters per second.

4. The volume of gas in a container at a constant temperature varies inversely as the pressure. If the volume is 32 cubic centimeters at a pressure of 8 pounds, find the pressure when the volume is 60 cubic centimeters.

5. The volume of a pyramid varies jointly as its height and the area of its base. A pyramid with a height of 12 feet and a base with area of 23 square feet has a volume of 92 cubic feet. Find the volume of a pyramid with a height of 17 feet and a base with an area of 27 square feet.

6. At top speed, a rabbit can cover 7 miles in 12 minutes. If a rabbit could continue at this rate indefinitely, how long would it take the rabbit to cross the 220-mile expanse of the Mojave Desert?

7. The current in a simple electrical circuit is inversely proportional to the resistance. If the current is 80 amps when the resistance is 50 ohms, find the current when the resistance is 22 ohms.

8. The volume of a cone varies jointly as its height and the square of its radius. A cone with a radius of 6 inches and a height of 10 inches has a volume of 120π cubic inches. Find the volume of a cone having a radius of 15 inches and a height of 7 inches.

9. The intensity of light produced by a light source varies inversely as the square of the distance from the source. If the intensity of light produced 3 feet from a light source is 750 foot-candles, find the intensity of light produced 5 feet from the same source.

10. Heather’s weekly pay is directly proportional to the number of hours she works at the record store. Her pay is $174 for 24 hours of work. Find the amount of pay for 40 hours of work.

11. A dishwasher uses 65 gallons of water to wash 5 loads of dishes. How many gallons of water would be used to wash 12 loads?

12. For a given interest rate, simple interest varies jointly as principal and time. If $2000 left in an account for 4 years earns interest of $320, how much interest would be earned in if you deposit $5000 for 7 years?

13. Wind resistance varies jointly as an object’s surface area and velocity. If an object traveling at 40 mile per hour with a surface area of 25 square feet experiences a wind resistance of 225 Newtons, how fast must a car with 40 square feet of surface area travel in order to experience a wind resistance of 270 Newtons?

14. Eduardo counted ten seconds between seeing lightning and hearing thunder, and he knew that the lightning was about 2 miles away. If he counted four seconds between the next flash of lightning and thunder, about how far away was the lightning?

15. The frequency of a vibrating guitar string varies inversely as its length. Suppose a guitar string 0.65 meters long vibrates 4.3 times per second. What frequency would a string 0.5 meters long have?

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