1. Ch 4: Solving & Graphing Inequalities G) Distance = rate x time Objective: To solve word problems involving distance, speed, and time.

2. Distance: Units include feet, yards, miles, meters, etc Rate/Speed: Units are in fraction format Definitions Time: Units include seconds, minutes, hours, days, etc. distance time ( ) Average Speed: The total distance traveled divided by the total time taken for a particular journey. Transitive Property: if a = b and b = c then a = c

3. Example of Unit Conversion The world record for the 100 yard dash is 9.4 seconds. How fast is this in miles/hr? Equivalent units 1 yard = 3 feet 5280 feet = 1 mile 60 seconds = 1 minute 60 minutes = 1 hour 100 yards = 9.4 seconds miles hr

4. Rules 1.Underline the numbers and units in the problems 2.THINK the problem through & DRAW a picture 3.Input the information into the table below 4.Solve each line using d = r  t convert units if necessary Note: distances can be added together. times can be added together. rates can NOT be added together! You must use d = r  t Same direction Opposite direction Round trip d = r  t

5. Example 1 Jane and her friends are driving to a cabin for the weekend. It is 150 miles away. If they drive 50 mi/hr, how long will it take them to get there? ? hrs 50 miles 1 hr 100 miles 2 hrs 3 hrs 150 miles

6. Example 1 Jane and her friends are going to a cabin for the weekend. It is 150 miles away. If they are drive 50 mi/hr, how long will it take them to get there? 150 mi 50mi/hrtSolve for t 150 mi =  t hr 50 mi hr 50 mi 50 mi hr 3 hr = t d = r  t Jane Table method

7. Example 1 Jane and her friends are driving to a cabin for the weekend. It is 150 miles away. If they drive 50 mi/hr, how long will it take them to get there? Her friend leaves one hour later. She wants to arrive at the same time as Jane. How fast must she drive? 50 miles 1 hr 100 miles 2 hrs ? miles 3 hrs 150 miles 75 miles 1 hr Same Direction

8. Example 1 150 mi 50 mi/hr3 3150 mi Same distance 150 mi =  (3 – 1)hr r 75 mi/hr = r 2 hr d = r  t r Solve for r Her friend leaves one hour later. She wants to arrive at the same time as Jane. How fast must she drive? Jane Her friend Table method Jane and her friends are going to a cabin for the weekend. It is 150 miles away. If they are drive 50 mi/hr, how long will it take them to get there? - 1

9. Example 2 1 hr2 hrs 3 hrs 3(r-20) mi A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the speed of the passenger train, if it overtakes the freight train in three hours. 4 hrs 4(r-20) mi 5 hrs 5(r-20) mi 3 hrs 3r mi 2(r-20) mi (r-20) mi 2 hrs 2r mi 1 hr r miles = Same Direction

10. Example 2 A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20 mph slower than the passenger train. Find the speed of the passenger train, if it overtakes the freight train in three hours. Passenger Freight d 3 3d d = r  t r Solve for r Same distance r+ 2- 20 d = r  3 PassengerFreight d = (r – 20)  (3 + 2) = 3r = 5r - 1003r -2r = -100r = 50 m/h Table method

11. 1) Classwork An aircraft carrier left Azores and traveled toward Madagascar at an average speed of 12 mph. A container ship left one hour later and traveled in the same direction at an average speed of 15 mph. How long did the aircraft carrier travel before the container ship caught up? d = r  t 5 hours 12d d Same distance 15- 1 t t Solve for t carrier container d = 12t carriercontainer d = 15(t – 1) 12t = 15t - 15 t =

12. 2)Daniel left the mall and traveled toward the mountains at an average speed of 30 mph. Joe left one hour later and traveled in the same direction at an average speed of 40 mph. How long did Daniel travel before Joe caught up? d = r  t 4 hours 30 d d Same distance 40- 1 t t Solve for t Daniel Joe d = 30t DanielJoe d = 40(t – 1) 30t = 40t - 40 t = Classwork

13. Example 3 Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet? 45 miles 14 miles 16 miles 1 hr 7 miles8 miles + ½ hr= 1.5 hrs Opposite Direction

14. Example 3 Two cyclists start at the same time from opposite ends of a course that is 45 miles long. One cyclist is riding at 14 mph and the second cyclist is riding at 16 mph. How long after they begin will they meet? Cyclist 1 Cyclist 2 d1d1 t t45 - d 1 d = r  t 14 Solve for t Same time 16 d 1 = 14  t Cyclist 1Cyclist 2 45 – d 1 = 16  t = 14t= 16t - 45 45 – d 1 = -16t + 45 d 1 14t = -16t + 45 t = 1.5 h Table method

15. Example 4 Maria left the White House at the same time as Trevon. They traveled in opposite directions. Trevon traveled at a speed of 39 mph. After two hours they were 140 miles apart. How fast did Maria drive? 140 miles 2r r 1 hr 39 miles 1 hr2 hrs 78 miles 2 hrs 78 +2r= 140 Opposite Direction

16. Example 4 Maria left the White House at the same time as Trevon. They traveled in opposite directions. Trevon traveled at a speed of 39 mph. After two hours they were 140 miles apart. How fast did Maria drive? Maria Trevon d1d1 2 2140 - d 1 d = r  t r Solve for r Same time 39 d 1 = r  2 MariaTrevon 140 – d 1 = 39  2 = 2r= 78 - 140 140 – d 1 = 62 d 1 2r = 62 r = 31 mph Table method

17. 3)An Air Force plane left Los Angeles and flew toward Jakarta at an average speed of 350 mph. A cargo plane left some time later flying in the opposite direction with an average speed of 260 mph. After the Air Force plane had flown for 11 hours the planes were 4630 miles apart. How long had the cargo plane been flying? d = r  t 3 hours 350d1d1 4630 - d 1 Same distance 260 11 t Solve for t Air Force cargo d = 350(11) Air Forcecargo 4630 - d = 260t 4630 - 3850 = 260t 4630 t = Classwork

18. 4)A diesel train left Bangalore and traveled west at an average speed of 85 mph. A freight train left two hours later and traveled in the opposite direction with an average speed of 35 mph. How many hours did the freight train travel before the trains were 890 miles apart? d = r  t t = 8 hours 85 d1d1 890 - d 1 Same distance 35 t t - 2 Solve for t - 2 diesel freight d = 85t dieselfreight 890 - d = 35(t - 2) 890 – 85t = 35t - 70 890 6 hours t – 2 = Classwork

19. Example 5 A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? 1 hr2 hrs3 hrs with current + 3 with current + 3 r r r d = 3r + 9 with current Round Trip

20. Example 5 A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? 3 hrs2 hrs1 hr against current − 3 miles against current − 3 miles 4 hrs against current − 3 miles d = 3r + 9 d = 4r − 12 with currentagainst current r − 3 Round Trip

21. Example 5 A boat travels for three hours with a current of 3 mph and then returns the same distance against the current in four hours. What is the boat's speed in calm water? with current against current d 3 4d d = r  t r Solve for r Same distance r3 d = (r + 3)  3 with currentagainst current d = (r – 3)  4 = 3r + 9 = 4r - 123r + 9 9 = r - 12r = 21 m/h 3+ - Table method

22. 5)Kathryn took a trip to City Hall and back. The trip there took two hours and the trip back took five hours. She averaged 36 mph faster on the trip there than on the return trip. What was Kathryn’s average speed on the trip there? d = r  t 60 mph r + 36 d d Same distance r 2 5 Solve for r + 36 there back d = (r + 36)  2 thereback d = 5r 2r + 72 = 5r r = 24 mph r + 36 = Classwork

23. 6)An aircraft carrier traveled to Madagascar and back. It took one hour longer to go there than it did to come back. The average speed on the trip there was 20 mph. The average speed on the way back was 25 mph. How long did it take for the aircraft carrier to fly to Madagascar? d = r  t 5 hours 20 d d Same distance 25 t + 1 t Solve for t + 1 to Madagascar back d = 20(t + 1) to Madagascarback d = 25t 20t + 20 = 25t t = 4 hours t + 1 = Classwork