Complete the following questions to practice the skills you have learned in this lesson.
1. If y varies directly as and , when . Find the equation that relates and .
2. The price, , that Eric pays for gas varies directly with the number of gallons, , he buys. It costs him $50 to buy 20 gallons of gas. Choose the equation that relates and .
3. Joseph is traveling on a road trip. The distance, , he travels before stopping for lunch varies directly with the speed, , he travels. He can travel 120 miles at a speed of 60 mph. How many miles would he travel before stopping for lunch at a rate of 65 mph?
4. The mass of a liquid, , varies directly with its volume, . A liquid with mass 16 kilograms has a volume of 2 liters. What is the volume, in liters, of this liquid if its mass is 128 kilograms?
5. The length, , that a spring stretches varies directly with a weight, , placed at the end of the spring. When Sarah placed a 10-pound watermelon on a hanging scale, the spring stretched 5 inches. What weight of watermelon, in pounds, would stretch the spring 6 inches?
6. The maximum load a beam, , will support varies directly with the square of the diagonal of the beam’s cross-section, . A beam with diagonal 6 inch will support a maximum load of 108 pounds. What load, in pounds, will a beam with a 10-inch diagonal support?
7. The number of calories, , burned varies directly with the amount of time, , spent exercising. Arnold burned 312 calories in 65 minutes exercising. How many calories would he burn if he exercises for 90 minutes?