Additional Exercises 8.7 Form I Applications Using Rational Equations and Variation
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1 Additional Exercises 8.7 Form I Applications Using Rational Equations and Variation 1. A cyclist bikes at a constant speed for 20 miles. He then returns 1. home at the same speed but takes a different route. His return trip takes one hour longer and is 25 miles. Find his speed 2. A boat travels 8 miles upstream and then back 8 miles in 3 hours. 2. The current of the river is 2 mph. What is the speed of the boat in still water? 3. Mark and Rachel both work for Smith Landscaping Company. 3. Mark can finish a planting job in 3 hours, while it takes Rachel 5 hours to finish the same job. If Mark and Rachel will work together on the job, and the cost of labor is $45 per hour, what should the labor estimate be? (Round to the nearest cent, if necessary.) 4. One pump can drain a pool in 7 minutes. When a second pump 4. is also used, the pool only takes 2 minutes to drain. How long would it take the second pump to drain the pool if it were the only pump in use? Find the missing length in the similar triangles x Solve the following variation problems. 6. y varies directly as x. y = 20 when x = 5. Find y when x = AE-299
2 7. y varies directly as x. y = 10 when x = 2. Find y when x = y varies inversely as x. y = 10 when x = 6. Find y when x = y varies inversely as x. y = 12 when x = 5. Find y when x = The amount of water used to take a shower is directly pro- 10. portional to the amount of time that the shower is in use. A shower lasting 21 minutes requires 12.6 gallons of water. Find the amount of water used in a shower lasting 10 minutes. 11. If the resistance in an electrical circuit is held constant, the 11. amount of current flowing through the circuit is directly proportional to the amount of voltage applied to the circuit. When 9 volts are applied to a circuit, 180 milliamperes of current flow through the circuit. Find the new current if the voltage is increased to 11 volts. 12. The amount of gas that a helicopter uses is directly proportional 12. to the number of hours spent flying. The helicopter flies for 4 hours and uses 48 gallons of fuel. Find the number of gallons of fuel that the helicopter uses to fly for 5 hours. AE-300
3 Additional Exercises 8.7 Form II Applications Using Rational Equations and Variation 1. A car travels 400 miles on level terrain in the same amount of 1. time it travels 160 miles on mountainous terrain. If the rate of the car is 30 miles per hour less in the mountains than on level ground, find its rate in the mountains. 2. A boat travels 9 kilometers upstream in the same amount of time. 2. it moves 16 kilometers downstream. If the rate of the current is 6 kilometers per hour, find the rate of the boat in still water. 3. In a race, Car A starts 1 mile behind Car B. Car A is. 3. traveling at 65 miles per hour, while Car B is traveling at 55 miles per hour. How long will it take for Car A to overtake Car B? 4. One conveyor belt can move 1000 boxes in 11 minutes. Another 4. can move 1000 boxes in 12 minutes. If another conveyor belt is added and all three are used, the boxes are moved in 3 minutes. How long would it take the third conveyor belt alone to do the same job? Find the missing length in the similar triangles x 20 Solve the following variation problems. 6. y varies directly as x. y = 25 when x = 3. Find y when x = AE-301
4 7. y varies directly as x. y = 8 when x = 2. Find y when x = y varies inversely as x. y = when x = 8. Find y when x = y varies inversely as x. y = 5 2 when x = 5 3. Find y when x = A person s hair length varies proportionately with the number 10. of weeks it has been growing. If Fred shaved his head bald and his hair was 0.2 inches long after 5 weeks, how long would it be after additional 6 weeks? (Round to the nearest hundredth of an inch.) 11. When the temperature stays the same, the volume of a gas is 11. inversely proportional to the pressure of the gas. If a balloon is filled with 145 cubic inches of a gas at a pressure of 14 pounds per square inch, find the new pressure of the gas if the volume is decreased to 29 cubic inches. 12. The amount of time it takes a swimmer to swim a race is 12. inversely proportional to the average speed of the swimmer. A swimmer finishes a race in 75 seconds with an average speed of 4 feet per second. Find the average speed of the swimmer if it takes 60 seconds to finish the race. AE-302
5 Additional Exercises 8.7 Form III Applications Using Rational Equations and Variation 1. The sports car travels 40 km/h faster than the loaded SUV and 1. trailer. While the SUV travels 150 km, the sports car goes 350 km. Find their speeds. 2. Jim can run 5 miles per hour on level ground on a still day. One 2. windy day, he runs 15 miles with the wind, and in the same amount of time runs 4 miles against the wind. What is the rate of the wind? 3. A painter can finish painting a house in 4 hours. Her assistant 3. takes 6 hours to finish the same job. How long would it take for them to complete the job if they were working together? 4. A baker can decorate the day s cookie supply four times as fast as 4. his new assistant. If they decorate all the cookies working together in 12 minutes, how long would it take for each of them to decorate the cookies working individually? Find the missing length in the similar triangles x Solve the following variation problems. 6. y varies directly as x. y = 0.7 when x = 0.4. Find y when x = AE-303
6 7. y varies directly as x. y = 400 when x = 125. Find y when 7. x = y varies inversely as x. y = 0.2 when x = 0.3. Find y when 8. x = y varies inversely as x. y = 6.25 when x = Find y when 9. x = If the voltage, V, in an electric circuit is held constant, the 10. current, I, is inversely proportional to the resistance, R. If the current is 120 milliamperes when the resistant is 5 ohms, find the current when the resistance is 30 ohms. 11. While traveling at a constant speed in a car, the centrifugal 11. acceleration passengers feel while the car is turning is inversely proportional to the radius of the turn. If the passengers feel an acceleration of 12 feet per second when the radius of the turn is 40 feet, find the acceleration the passengers feel when the radius of the turn is 120 feet. 12. The length a spring stretches is directly proportional to the force 12. applied. If a force of 5 pounds stretches a spring 3 inches, how much force is necessary to stretch the same spring 10 inches? AE-304
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