t = 5 x = 9 x = 6/5 Solve ANSWER How long would it take you To travel 2 miles going 60mph?. 2 minutes

Rate, Time, & Distance Problems Objective Solve word problems involving uniform motion

Uniform Motion If something is moving with UNIFORM MOTION it is moving at a speed that is not changing. The speed stays constant through the entire trip. When solving word problems that talk about distance traveled, rate of speed, and the time it takes to make a trip, you should: 1) set up a chart, 2) use the distance formula, and 3) draw a picture.

Rate Problems What distance would you travel in 6 hours at 60 mi/hr? Using the distance formula you can find out. The distance is unknown (d). The time is 6 hours, so, t = 6. The rate is 60 mi/h, so r = 60. r x t = d 60 x 6 = d d = 360 miles rate  time = distance  rt = d

Rate Problems What is the average rate of speed if 275 miles are traveled in 5.5 hours? The distance is 275 miles, so d =275. The time is 5.5 hours, so t = 5.5. The rate is what you need to find. r x t = d r x 5.5 = 275 d = 50 miles/hour rate  time = distance  rt = d

Rate Problems How long does it take to travel 288miles at an average rate of 72 mph? The distance is 288, so d = 288. The rate is 72 mi/h so, r = 72. The time is what you need to find. r x t = d 72 x t = 288 d = 4 hours rate  time = distance  rt = d

There are 3 common types of uniform motion problems. Motion in opposite directions Motion in the same direction A round trip If it’s OPP, then ADD If it is not OPP, then set Equally Opposite direction add them together All others, set equal to each other

How to Set up the Chart RateTimeDistance Motion #1 Motion #2 rate  time = distance  rt = distance

MJ and Peter Parker leave school traveling in opposite directions. Peter is walking and MJ is biking, averaging 6 km/h more than Peter. If they are 18km apart after 1.5 h, what is the rate of each? RateTimeDistance MJ Peter 6 + x x x If it’s OPP, then ADD!! x 1.5x1.5x MJ and Peter Parker leave school traveling in opposite directions. Peter is walking and MJ is biking, averaging 6 km/h more than Peter. If they are 18km apart after 1.5 h, what is the rate of each? += 18 MJ- 9km/h Peter-3km/h

Carla begins biking south at 20 km/h at noon. Dean leaves from the same point 15 min. later to catch up with her. If Dean bikes at 24 km/h, how long will it take him to catch up with Carla? RateTimeDistance Carla Dean x x – ¼ 20x If it’s NOT OPP, then set equally!! 20x 24x - 624x - 6 Carla begins biking south at 20 km/h at noon. Dean leaves from the same point 15 min. later to catch up with her. If Dean bikes at 24 km/h, how long will it take him to catch up with Carla? = 15min = ¼ hour 1¼ or 1 hour 15 min

Mark drove his car to the garage at 48 km/h and then walked back home at 8 km/h. The drive took 10 min less than the walk home. How far did Mark walk and for how long? RateTimeDistance There Back 48 8x 48x - 8 If it’s NOT OPP, then set equally!! 48x - 8 8x8x Mark drove his car to the garage at 48 km/h and then walked back home at 8 km/h. The drive took 10 min less than the walk home. How far did Mark walk and for how long? = Distance = 1 3/5 mile Time = 1/5 or 12 min 10min = 1/6 hour x – 1/6