(For help, go to Lesson 1-1.) ALGEBRA 1 LESSON 4-8 Write a variable expression for each situation. 1.value in cents of q quarters 2.twice the length 3.number of miles traveled at 34 mi/h in h hours 4.weight of 5 crates if each crate weighs x kilograms 5.cost of n items at $3.99 per item Equations and Problem Solving 4-8

Solutions 1.value in cents of q quarters: 25q 2.twice the length : 2 3.number of miles traveled at 34 mi/h in h hours: 34h 4.weight of 5 crates if each crate weighs x kilograms: 5x 5.cost of n items at $3.99 per item: 3.99n Equations and Problem Solving ALGEBRA 1 LESSON

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 on parallel altitudes. 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 ALGEBRA 1 LESSON

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. Equations and Problem Solving ALGEBRA 1 LESSON (continued) =Divide each side by –150. –150t –150 –330 –150 t =2Simplify t – 1 = The jet will catch up with the airplane in 1 h. 1515

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 uphillequals distance downhill Part of hikeRateTimeDistance hiked Uphill4x4x Downhill63 – x6(3 – x) Write:4 x= 6( 3 – x ) Equations and Problem Solving ALGEBRA 1 LESSON

4x=6(3 – x) 4x=18 – 6xUse the Distributive Property. 4x + 6x=18 – 6x + 6xAdd 6x to each side. 10x=18Combine like terms. Equations and Problem Solving ALGEBRA 1 LESSON (continued) =Divide each side by x x=1Simplify Your trip uphill was 1 h long. 4545

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 (x + 50) Equations and Problem Solving ALGEBRA 1 LESSON

2x + 2(x + 50)=2500 2x + 2x + 100=2500Use the Distributive Property. 4x + 100=2500Combine like terms. 4x – 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. Equations and Problem Solving ALGEBRA 1 LESSON (continued) =Divide each side by 4. 4x44x

1.The sum of three consecutive integers is 117. Find the integers. 2.You and your brother started biking at noon from places that are 52 mi apart. You rode toward each other and met at 2:00 p.m. Your brother’s average speed was 4 mi/h faster than your average speed. Find both speeds. 3.Joan ran from her home to the lake at 8 mi/h. She ran back home at 6 mi/h. Her total running time was 32 minutes. How much time did it take Joan to run from her home to the lake? 38, 39, 40 your speed: 11 mi/h; brother’s speed: 15 mi/h about 13.7 minutes Equations and Problem Solving ALGEBRA 1 LESSON