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Chapter 3: Solving Equations

Chapter 3: Solving Equations. 3.6 Equations & Problem Solving. Example 1. The length of a rectangle is 6 in more than its width. The perimeter of the rectangle is 24 in. What is the length of the rectangle?. Example 1a.

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Chapter 3: Solving Equations

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  1. Chapter 3: Solving Equations 3.6 Equations & Problem Solving

  2. Example 1 • The length of a rectangle is 6 in more than its width. The perimeter of the rectangle is 24 in. What is the length of the rectangle?

  3. Example 1a • The width of a rectangle is 2 cm less than its length. The perimeter of the rectangle is 16 cm. What is the length of the rectangle?

  4. Consecutive integers • Consecutive: • One right after another • Consecutive integers: -2, -1, 0, 1, 2,… • Consecutive even integers: -2, 0, 2, 4,… • Consecutive odd integers: -3, -1, 0, 1, 3…

  5. Example 2 • The sum of three consecutive integers is 147. Find the integers.

  6. Example 2a • The sum of three consecutive integers is 48. Find the three integers.

  7. Uniform Motion • Object that moves at a constant rate (think cruise control) • Formula: d = r t

  8. Example 3 • A train leaves a train station at 1 p.m. It travels at an average rate of 72 mph. A high-speed train leaves the same station an hour later. It travels at an average rate of 90 mph. The second train follows the same route as the first train on a track parallel to the first. In how many hours will the second train catch up with the first train?

  9. Example 3a • A group of campers and one group leader left a campsite in a canoe. They traveled at an average rate of 10 km/h. Two hours later, the other group leader left the campsite in a motorboat. He traveled at an average rate of 22 km/h. • How long after the canoe left the campsite did the motorboat catch up with it? • How long did the motorboat travel?

  10. Example 4 • Noya drives into the city to buy a software program at a computer store. Because of traffic conditions, she averages only 15 mph. On her drive home she averages 35 mph. If the total travel time is 2 hours, how long does it take her to drive to the computer store?

  11. Example 4a • On his way to work from home, your uncle averaged only 20 mph. On his drive home, he averaged 40 mph. If the total travel time was 1.5 hours, how long did it take him to drive to work?

  12. Example 5 • Jane and Peter leave their home traveling in opposite directions on a straight road. Peter drives 15 mph faster than Jane. After 3 hours, they are 225 miles apart. Find Peter’s rate and Jane’s rate.

  13. Example 5a • Sarah and John leave Perryville traveling in opposite directions on a straight road. Sarah drives 12 mph faster than John. After 2 hours, they are 176 miles apart. Find Sarah’s speed and John’s speed.

  14. Homework • P. 162 • 2-20 even

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