PROBLEM SOLVING WITH INVERSE VARIATION
1. At a constant temperature, pressure P in pounds per square inch and volume V in cubic inches of an ideal gas are related by inverse variation. That is, PV = k, for some nonzero constant k. A gas with volume 30 cubic inches is under a pressure that is 40 pounds per square inch. Find the pressure when the volume is 60 cubic inches.
2. Samantha and Derek plan to bicycle a distance of 8 miles. What is their speed if they complete the trip in ¼ hour? In ½ hour? In 1 hour? In 2 hours? In 3 hours? In 4 hours?
3. Given a fixed number as the area of a rectangle, length varies inversely as the width. What happens to the length of a rectangle if area is constant and the width is doubled?
4. The pitch of a musical tone varies inversely as its wavelength. If one tone has a pitch of 440 vibrations per second and a wavelength of 2.4 feet, find the wavelength of a tone that has a pitch of 660 vibrations per second.
5. Pam and Adam are seated on the same side of a seesaw. Pam is 6 feet from the fulcrum and weighs 115 pounds. Adam is 8 feet from the fulcrum and weighs 120 pounds. Kam is seated on the other side of the seesaw, 10 feet from the fulcrum. If the seesaw is balanced, how much does Kam weigh?
6. A 200-pound weight is located 5 feet from the fulcrum. How far from the fulcrum should 125 pounds be placed to balance the lever?
7. A lever has a 250-kg rock on one end. The fulcrum is 8 cm from the rock and 100 cm from the other end. What does the weight of the other object have to be if the lever is balanced?
8. Marcie weighs 133 pounds and sits 6 feet from the fulcrum of a seesaw. She balances with Rosalind if Rosalind sits 7 feet from the fulcrum. How much does Rosalind weigh?
9. It takes 16 hours for 2 people to resurface a gym floor. How long would it take 6 people?
10. It takes 4 hours for 9 cooks to prepare a school lunch. How long would it take 8 cooks to prepare the lunch?
11. The volume V of a gas varies inversely as the pressure P upon it. The volume of a gas is 200 cubic centimeters under a pressure of 32 kg/cm2. What will be its volume under a pressure of 20 kg/cm2 ?
12. It takes five hours for two washing machines to wash a fixed amount. How long would it take for ten washing machines to wash the same amount of clothes?