Solve. 1. 2. ANSWER x = 9 ANSWER t = 5 3. 4. How long would it take you To travel 2 miles going 60mph?. ANSWER x = 6/5 ANSWER 2 minutes

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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? rate  time = distance  rt = d 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 Problems rate  time = distance  rt = d 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 Problems rate  time = distance  rt = d 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

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 Rate Time Distance Motion #1 Motion #2 rate  time = distance  rt = distance Rate Time Distance Motion #1 Motion #2

MJ 6 + x 9 + 1.5x 9 + 1.5x 1.5 Peter x 1.5 1.5x 1.5x + = 18 MJ- 9km/h 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? 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? Rate Time Distance MJ 6 + x 9 + 1.5x 9 + 1.5x 1.5 Peter x 1.5 1.5x 1.5x If it’s OPP, then ADD!! + = 18 MJ- 9km/h Peter-3km/h

15min = ¼ hour Carla 20 20x 20x x Dean 24 x – ¼ 24x - 6 24x - 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? 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 Rate Time Distance Carla 20 20x 20x x Dean 24 x – ¼ 24x - 6 24x - 6 If it’s NOT OPP, then set equally!! = 1¼ or 1 hour 15 min

10min = 1/6 hour There 48 x – 1/6 48x - 8 48x - 8 Back 8 x 8x 8x = 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? 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? 10min = 1/6 hour Rate Time Distance There 48 x – 1/6 48x - 8 48x - 8 Back 8 x 8x 8x If it’s NOT OPP, then set equally!! = Distance = 1 3/5 mile Time = 1/5 or 12 min