4.7 Uniform Motion (work).notebook November 15, UNIFORM MOTION

Transcription

1 4.7 UNIFORM MOTION When an object moves at a constant speed, or rate, it is said to be in uniform motion. The formula d = rt is used to solve uniform motion problems. Example 1 An airplane flies 1000 miles due east in 2 hours and 1000 miles due south in 3 hours. What is the average speed of the airplane? Example 2 Lisa and Michael traveled 2 miles in 1/2 hour. What was their rate?

2 Example 3 Don and Donna Wyatt leave their home at the same time, traveling in opposite directions. Don travels at 80 kilometers per hour and Donna travels at 72 kilometers per hour. In how many hours will they be 760 kilometers apart? Example 4 Suppose John and Gina leave at the same time traveling in the same direction. Gina drives at a rate of 85 km/h and John at 70 km/h. How long until they are 90 km apart?

3 Example 5 At 8:00 a.m. Felicia leaves home on a business trip driving 35 miles per hour. A half hour later, Jose' discovers that Felicia forgot her briefcase. He drives 50 miles per hour to catch up with her. If Jose' is delayed 15 minutes with a flat tire, when will he catch up with Felicia? Example 6 Jamie left home on his bicycle for a long-distance ride. Mary left 3 hours later on her motorcycle carrying his lunch. Mary traveled at 42 mph and she caught Jamie in 1.5 hours. How fast was Jamie traveling?

4 Practice Problem 1 At 1:30 p.m., an airplane leaves Tuscon for Baltimore, a distance of 2240 miles. The plane flies at 280 miles per hour. A second airplane leaves Tuscon at 2:15 p.m., and is scheduled to land in Baltimore 15 minutes before the first airplane. At what rate must the second airplane travel to arrive on schedule? Practice Problem 2 Two trains leave York at the same time, one traveling north, the other south. The first train travels at 40 miles per hour and the second at 30 miles per hour. In how many hours will the trains be 245 miles apart?

5 Practice Problem 3 Rosita drove from Boston to Cleveland, a distance of 616 miles, to visit her grandparents. Her rest, gasoline, and food stops took 2 hours. What was her average speed if the trip took 16 hours altogether? Practice Problem 4 Two cyclists are traveling in the same direction on the same bike path. One travels at 20 miles per hour and the other at 14 miles per hour. After how many hours will they be 15 miles apart?

6 Practice Problem 5 At the same time Kris leaves Washington, D.C. for Detroit, Amy leaves Detroit for Washington, D.C. The distance between the cities is 510 miles. Amy's average speed is 5 miles per hour faster than Kris's. How fast is Kris driving if they pass each other in 6 hours? Practice Problem 6 The Harvest Moon leaves the pier at 9:00 a.m. at 8 knots (nautical miles per hour). A half hour later, The River Nymph leaves the same pier in the same direction traveling at 10 knots. At what time will The River Nymph overtake The Harvest Moon?

7 Practice Problem 7 Art leaves at 10:00 a.m., traveling at 50 miles per hour. At 11:30 a.m., Jennifer starts in the same direction at 45 miles per hour. When will they be 100 miles apart? Practice Problem 8 Guillermo is driving 40 miles per hour. After he has driven 30 miles, his brother Jorge starts driving in the same direction. At what rate must Jorge drive to catch up with Guillermo in 5 hours?

8 Practice Problem 9 Two airplanes leave Dallas at the same time and fly in opposite directions. One airplane travels 80 miles per hour faster than the other. After three hours, they are 2940 miles apart. What is the rate of each airplane? Practice Problem 10 An express train travels 80 kilometers per hour from Wheaton to Ward. A local train, traveling at 48 kilometers per hour, takes 2 hours longer for the same trip. How far apart are Wheaton and Ward?