1. Algebra 1 The width of a rectangle is 3 in. less than its length. The perimeter of the rectangle is 26 in. What is the width of the rectangle?

2. Algebra 1 The sum of three consecutive integers is 72. Find the integers. Equations and Problem Solving Lesson 3-6 Additional Examples

3. Algebra 1 An airplane left an airport flying at 180 mi/h. A jet that flies at 330 mi/h left 1 hour later. The jet follows the same route as the airplane at a different altitude. How many hours will it take the jet to catch up with the airplane? AircraftRateTimeDistance Traveled Airplane180t180t Jet330t – 1330(t – 1) Define:Let t = the time the airplane travels. Then t – 1 = the time the jet travels. Equations and Problem Solving Lesson 3-6 Additional Examples

4. Algebra 1 Relate:distance traveledequalsdistance traveled by airplaneby jet Write:180 t=330( t – 1 ) 180t=330(t – 1) 180t=330t – 330Use the Distributive Property. 180t – 330t=330t – 330 – 330tSubtract 330t from each side. –150t=–330Combine like terms. (continued) –150t –150 –330 –150 =Divide each side by –150. t =2Simplify. 1515 t – 1 =1 1515 The jet will catch up with the airplane in 1 h. 1515 Equations and Problem Solving Lesson 3-6 Additional Examples

5. Algebra 1 Suppose you hike up a hill at 4 km/h. You hike back down at 6 km/h. Your hiking trip took 3 hours. How long was your trip up the hill? Define:Let x = time of trip uphill. Then 3 – x = time of trip downhill. Relate: distance uphill equalsdistance downhill Part of hikeRateTimeDistance hiked Uphill4x4x Downhill63 – x6(3 – x) Write:4 x= 6( 3 – x ) Equations and Problem Solving Lesson 3-6 Additional Examples

6. Algebra 1 4x=6(3 – x) 4x=18 – 6xUse the Distributive Property. 4x + 6x=18 – 6x + 6xAdd 6x to each side. 10x=18Combine like terms. (continued) =Divide each side by 10. 10x 10 18 10 x=1.8Simplify. Your trip uphill was 1.8 h long. Equations and Problem Solving Lesson 3-6 Additional Examples

7. Algebra 1 Two jets leave Dallas at the same time and fly in opposite directions. One is flying west 50 mi/h faster than the other. After 2 hours, they are 2500 miles apart. Find the speed of each jet. Define:Let x = the speed of the jet flying east. Write: 2 x + 2( x + 50 ) = 2500 Then x + 50 = the speed of the jet flying west. Relate:eastbound jet’s plus westbound jet’s equals the total distance distance distance JetRateTimeDistance Traveled Eastboundx22x Westboundx + 5022(x + 50) Equations and Problem Solving Lesson 3-6 Additional Examples

8. Algebra 1 2x + 2(x + 50)=2500 2x + 2x + 100=2500Use the Distributive Property. 4x + 100=2500Combine like terms. 4x + 100 – 100=2500 – 100Subtract 100 from each side. 4x=2400Simplify. x=600 x + 50=650 The jet flying east is flying at 600 mi/h. The jet flying west is flying at 650 mi/h. (continued) =Divide each side by 4. 4x44x4 2400 4 Equations and Problem Solving Lesson 3-6 Additional Examples

9. Algebra 1 Classwork/Homework Work sheet