Direct & Inverse Variation Application Problems

Direct Variation Applications 1. The height of a wave in California varies directly with the seconds that pass by. At 4 seconds, the wave is 6 feet high. Find the constant of variation k. Be sure to show your work. 2. Weight varies directly with gravity. If Buzz Aldrin weighed 360 pounds on earth but only 60 pounds on the moon, what is the weight of a person who weighed 54 pounds on the moon? 3. The number of calories in a muffin is directly proportional to the amount of sugar in the muffin. If a 200 calorie muffin has 500 grams of sugar, how many calories are in a muffin with 2,075 grams of sugar? 4. In scuba diving, the time it takes a diver to ascend safely to the surface varies directly with the depth of the dive. If it takes 0.75 minutes to reach the surface from a 45 foot dive, determine the time it will take to reach the surface from a 120 foot dive. Inverse Variation Applications 5. The number of hours it takes for a block of ice to melt varies inversely as the temperature. If it takes 2 hours for a square inch of ice to melt at 65º, find the constant of variation. 6. The width of a rectangle varies inversely with its length. If the width is 4 when the length is 12, find the width when the length is 16. 7. The pitch of a musical note varies inversely as its wavelength. If the tone has a pitch of 440 vibrations per second and a wavelength of 2.4 feet, find the pitch of a note that has a wavelength of 1.6 feet. 8. In kick boxing, it is found that the force needed to break a board, varies inversely with the length of the board. If it takes 5 lbs of pressure to break a board 2 feet long, how many pounds of pressure will it take to break a board that is 8 feet long? 9. When air is pumped into an automobile tire, the pressure is inversely proportional to the volume. If the pressure is 35 pounds when the volume is 120 cubic inches, what is the pressure when the volume is 140 cubic inches? 10. Sketch a basic graph of a) a direct variation relationship and b) an inverse variation relationship.