Tuesday’s Warm Up Simplify : 7 3 2 5 x 6 7 3 x 4 11x 7 310x 12 21x 28 11x 7 311x 16 11x 7 33x 48 11x 44 x 41 Motion Problem Set Ups 1. A passenger train’s speed is 60 mi/h, and a freight train’s speed is 40 mi/h. The passenger train travels the same distance in 1.5 h less time than the freight train. How long does each train take to make the trip? Rate Time Distance Pass. Train 60mph t 1.5 60 t 1.5 Frght. Train 40mph t 40 t 60 t 1.5 40 t Motion Problem Set Ups 2. Marla begins walking at 3 mi/h toward the library. Her friend meets her at the halfway point and drives her the rest of the way to the library. The distance to the library is 4 miles. How many minutes did Marla walk? 1st Half 2nd Half Rate Time Distance 3mph t 2mi ? ? 2mi 3t 2 Motion Problem Set Ups 3. Lois rode her bike to visit a friend. She traveled at 10 mi/h. While she was there, it began to rain. Her friend drove her home in a car traveling at 25 mi/h. Lois took 1.5 h longer to go to her friend’s than to return home. How many hours did it take Lois to ride to her friend’s house? Rate Time Distance to by bike 10mph t 1.5 10 t 1.5 home by car 25mph t 25 t 10 t 1.5 25 t Motion Problem Set Ups 4. Fred begins walking toward John’s house at 3 mi/h. John leaves his house at the same time and walks toward Fred’s house on the same path at a rate of 2 mi/h. How long will it be, in minutes, before they meet if the distance between the houses is 4 miles? Rate Time Distance Fred 3mph t 3t John 2mph t 2 t 3 t 2 t 4 Motion Problem Set Ups 5. May rides her bike the same distance that Leah walks. May rides her bike 10 km/h faster than Leah walks. If it takes May 1 h and Leah 3 h to travel that distance, how fast does each travel? Rate Time Distance May r 10 1hr r 10 Leah r 3hr 3 r 60 r 1.5 40 r Motion Problem Set Ups 6. A train leaves the station at 6:00 P.M. traveling west at 80 mi/h. On a parallel track, a second train leaves the station 3 hours later traveling west at 100 mi/h. At what time will the second train catch up with the first? Rate Time Distance First Train 80mph t 80t Second Train 100mph t 3 100 t 3 80 t 100 t 3 Motion Problem Set Ups 7. At 10:00 A.M., a car leaves a house at a rate of 60 mi/h. At the same time, another car leaves the same house at a rate of 50 mi/h in the opposite direction. At what time will the cars be 330 miles apart? Rate Time Distance First Car 60mph t 60t Second Car 50mph t 50t 60t 50t 330 Motion Problem Set Ups 8. It takes 1 hour longer to fly to St. Paul at 200 mi/h than it does to return at 250 mi/h. How far away is St. Paul? Rate Time Distance Fly to St. Paul 200mph t 1 200 t 1 Rtn from St. Paul 250mph t 250t 200 t 1 250t Tuesday Night’s Homework Solve Each of today’s worksheet problems Wednesday Warm Up The Charlestown Chiefs football team scored 10 times for a total of 46 points. If a touchdown is worth 7 points and a field goal is worth 3 points, how many touchdowns and how many field goals did the Chiefs score? # of Touchdowns: x # of Field Goals: 10 x # of Touchdowns: 4 # of Field Goals: 6 7 x 310 x 46 7 x 30 3x 46 4 x 30 46 4 x 16 x4 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. How are the distances that the two jets fly related Distance flown by 1st Jet + Distance flown by 2nd jet = 2500 mi 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. How are the times that the two jets fly related The time of flight of 1st Jet = The time of flight of 2nd Jet 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. How are the speeds of the two jets fly related Speed of Westbound Jet = Speed of Eastbound Jet + 50 mi/hr 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. Then x + 50 = the speed of the jet flying west. Relate: eastbound jet’s plus westbound jet’s equals the total distance distance distance Jet Eastbound Rate x Westbound x + 50 Write: 2 x Time Distance Traveled 2 2x 2 2(x + 50) + 2( x + 50 ) Eastbound Westbound = 2500 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. 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. Jet Rate Eastbound x Westbound x + 50 Time Distance Traveled 2 2x 2 2(x + 50) 2 x 2 x 100 2500 4 x 100 2500 Eastbound Westbound Westbound Jet: 650mph 4 x 2400 x 600mph Eastbound Jet: 600mph 1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart? Rate Northbound Southbound Time Distance 1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart? Northbound Southbound Rate 83 mph 67 mph Time Distance 1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart? Northbound Southbound Rate 83 mph 67 mph Time t t Distance 1. Two trains left Mooseport at the same time. One traveled north at 83 mph. The other traveled south at 67 mph. After how many hours were the two trains 600 miles apart? Northbound Southbound Rate 83 mph 67 mph Time t t Distance 83t 67t 83t 67t 600 2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet? Rate Time Distance Romeo Juliet 2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet? Rate Time Distance Romeo 5 m/s Juliet 4 m/s 2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet? Rate Time Distance Romeo 5 m/s t Juliet 4 m/s t -3 2. Romeo first saw Juliet when she was 87 meters away. He started running toward her at a rate of 5 m/s. Three seconds later, Juliet saw Romeo and began running toward him at a rate of 4 m/s. How many seconds after Romeo first saw Juliet did they meet? Rate Time Distance Romeo 5 m/s t 5t Juliet 4 m/s t -3 4(t - 3) 5t 4 t 3 87 3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up? Rate Time Distance Bad Bart Police Helo 3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up? Rate Time Distance Bad Bart 70 mph Police Helo 100 mph 3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up? Rate Time Distance Bad Bart 70 mph t Police Helo 100 mph t - .5 3. Bad Bart is fleeing the scene of a bank robbery at 70 mph. Thirty minutes after he leaves, a police helicopter leaves the scene to catch him, traveling 100 mph along the same route. How many hours will Bart have been traveling when the police catch up? Rate Time Distance Bad Bart 70 mph t 70t Police Helo 100 mph t - .5 100(t - .5) 70t 100 t .5 4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go? Rate Uphill Downhill Time Distance 4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go? Uphill Downhill Rate 4 mph 30 mph Time Distance 4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go? Uphill Downhill Rate 4 mph 30 mph Time t 3-t Distance 4. Karma rode her bike up a mountain trail at an average speed of 4 mph. Then she rode back down the trail at an average speed of 20 mph. The entire trip took 3 hours. How far up the mountain did Karma go? Uphill Downhill Rate 4 mph 30 mph Time t 3-t Distance 4t 30(3 - t ) 4t 30 3 t Wednesday Night’s Homework Complete a D = RT table for each problem. Then use the table to construct an equation. Thursday Warm Up Solve each of the problems from last night’s homework. 1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart? Rate Time Distance Camel #1 Camel #2 1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart? Rate Time Distance Camel #1 9 km/hr Camel #2 7 km/hr 1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart? Rate Time Distance Camel #1 9 km/hr t Camel #2 7 km/hr t 1. Two camels pass each other in the desert, going in opposite directions. One camel is walking at an average rate of 9 km/h. The other camel is walking at an average rate of 7 km/h. After how many hours will the camels be 60 km apart? Rate Time Distance Camel #1 9 km/hr t 9t Camel #2 7 km/hr t 7t 9t 7t 60 2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel. Rate Camel #1 Camel #2 Time Distance 2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel. Camel #1 Camel #2 Rate r km/hr (r + 3)km/hr Time Distance 2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel. Camel #1 Camel #2 Rate r km/hr (r + 3)km/hr Time 4 hr 4 hr Distance 2. Two camels pass each other in the desert, going In opposite directions. The rate of one camel is 3 km/h faster than the rate of the other. Four hours later, the camels are 68 km apart. Find the rate of the faster camel. Camel #1 Camel #2 Rate r km/hr (r + 3)km/hr Time 4 hr 4 hr Distance 4r 4(r +3) 4r 4 r 3 68 3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first? Rate Time Distance 1st Plane 2nd Plane 3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first? Rate Time Distance 1st Plane 270 mph 2nd Plane 450 mph 3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first? Rate Time Distance 1st Plane 270 mph t 2nd Plane 450 mph t-2 3. A plane left Emerald City flying at an average rate of 270 mph. Two hours later, another plane left Emerald City flying in the same direction at 450 mph. How long will the second plane be flying until it catches up with the first? Rate Time Distance 1st Plane 270 mph t 270t 2nd Plane 450 mph t-2 450(t - 2) 270t 450 t 2 4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles. Rate Eastbound Westbound Time Distance 4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles. Eastbound Westbound Rate 420 mph 350 mph Time Distance 4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles. Eastbound Westbound Rate 420 mph 350 mph Time t t- 2 Distance 4. At 9:00 AM, a jet leaves St. Louis and travels east at 420 mph. At 11:00 AM, another jet leaves St. Louis and travels west at 350 mph. What time will the two jets be 3535 miles. Eastbound Westbound Rate 420 mph 350 mph Time t t- 2 Distance 420t 350(t - 2) 420t 450 t 2 3535 Thursday Homework Study for uniform motion quiz by doing practice problems