Chapter Eight:  Systems of Equations

Take notes on the following topics.

Chapter Eight

Section 8.1

Section 8.2

Section 8.3

Section 8.4

Section 8.5

Section 8.6

Back to Mrs. Leary's Math Web Page or Back to Algebra Contents

Section 8.5   Motion Problems

(Examples provided by Prentice Hall)

 

Example 1		Bud takes a leisurely stroll. He walks at a constant rate of two miles per hour. Carrie starts out for a brisk walk one hour later. She walks at a constant rate of 3 miles per hour. How long will it take for Carrie to catch up with Bud? Let t be the time in hours that Carrie walks. Let d be the distance in miles that they each walked.   Distance Rate Time Bud d 2 t + 1 Carrie d 3 t d = 2(t + 1) d = 3t Substituting, 2(t + 1) = 3t 2t + 2 = 3t 2 = t They meet after Carrie walks for 2 hours.
Example 2	Antonio is riding on a train. He gets up from his seat and walks forward. As he walks, he travels 1.1 miles in two minutes. As he walks back to his seat, he travels 0.9 miles in 2 minutes. How fast was the train moving, and how fast did Antonio walk inside the train? Let s be Antonio's walking speed inside the train, in miles per minute. Let t be the speed of the train, in miles per minute.   Distance Rate Time Forward 1.1 t + s 2 Return 0.9 t – s 2 2(t + s) = 1.1     (1) 2(t – s) = 0.9 (2) 2t + 2s = 1.1     (1) 2t – 2s = 0.9 (2) Add. 4t = 2.0 t = 0.5 The train travels 0.5 miles per minute. Subtract (2) from (1). 4s = 2.0 s = 0.05 Antonio walks 0.05 miles per minute.
Example 3	Alan has challenged Sam to a duel with water pistols at 50 feet. They start walking in opposite directions. Alan walks at 2 feet per second. Sam runs at 6 feet per second. How long will it take them to be 50 feet apart? Let t be the time, in seconds, for them to be 50 feet apart. Let d be the distance between them, which is 50 feet. rt = d (2 + 6)t = 50 8t = 50 t = 50/8 or   6 1/4 They are 50 feet apart in 6 1/4 seconds.