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Unit 2, Week 5 – Fastest Rate, Multi-Trip and Average Distance, Rate and Time Problems

Unit 2, Week 5 – Fastest Rate, Multi-Trip and Average Distance, Rate and Time Problems. Do Now – (√100), (1 2 ), (6 x 2). Please pick up your guided notes and respond to the following SILENTLY & INDEPENDENTLY: Convert 35 minutes into hours.

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Unit 2, Week 5 – Fastest Rate, Multi-Trip and Average Distance, Rate and Time Problems

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  1. Unit 2, Week 5 – Fastest Rate, Multi-Trip and Average Distance, Rate and Time Problems

  2. Do Now – (√100), (12), (6 x 2) Please pick up your guided notes and respond to the following SILENTLY & INDEPENDENTLY: Convert 35 minutes into hours. Quinton is trying to figure out if he has enough time to make it to the football game tonight. The game is at 5:00 and his mom is taking him at 4:20. If his mom drives at 55 mph and the game is 22 miles away, will he make it on time?

  3. Weekly Agenda Monday – Fastest Rate & Multi-Trip Problems Tuesday/Wednesday – Discovery Testing & Average Rate Problems Thursday – Unit Test Review Friday – Unit 2 Test

  4. Today’s Agenda Do Now – 8 minutes Shout Outs – 2 minutes Class Averages/Tracking – 3 minutes Student of the Week – 1 minute Weekly/Today Agenda – 1 minute Word Problem Investigation Group Work – 10 minutes GP & IP Group Work – 15 minutes Exit Ticket – 5 minutes

  5. Today’s Objective SWBAT solve multi-trip distance, rate, and time problems and compare distances, rates, and times.

  6. Distance, Rate, and Time To end the unit this week, we will be working with multi-step distance, rate, and time time word problems to find the average rate, fastest rate, or a missing part of a trip. To begin today, you will be working in groups to apply your knowledge of last week’s objectives to solve the problems.

  7. Distance, Rate, and Time Investigation You are in groups of 4. Together, you will work together to try to solve the problem given to you. You may use your notes, your partners, and your calculators. Together, you CAN solve the problem – Use your equations and knowledge! I will be cycling around to monitor your progress and check your final answers.

  8. Distance, Rate, and Time Example 1: Melanie is practicing for a swim meet. Four of her practice results are shown in the table. For which distance did Melanie swim the fastest?

  9. Distance, Rate, and Time • Example 1: • For which distance did Melanie swim the fastest? • Find the rates for each of the distance using r = d/t. • When d =50, 50/56 = r = 0.89 m/s • When d = 100, 100/130 r = 0.77 m/s • When d = 200, 200/184 r = 1.09 m/s • When d = 400, 400/345 r = 1.16 m/s • Compare the following distances and find the fastest distance. • Her fastest rate was 1.16 m/s and that goes with a distance of 400 m.

  10. Distance, Rate, and Time • Example 2: • The table shows distances and rates for different car race trials. Which rate provided the shortest time? • Find the times for each of the rates using t=e/r • When r = 60, 300/60 t = 5 hours • When r = 68, 35/68 t = 0.5 hours • When r = 72, 120/72 t = 1.6 hours • When r = 80, 220/80 t = 2.75 hours • Compare the following rates and find the fastest time. • The shortest time was 0.5 hours, which went with 68 mph.

  11. Distance, Rate, and Time Example 3: The following chart shows rates and times for different scooters. For which rate did the scooters travel the shortest distance?

  12. Distance, Rate, and Time Example 4: The following times are paired with distances from a 24 hour bicycling race. What time had the the fastest rate?

  13. Distance, Rate, and Time Example 5: The following table displays rates and times. For which rate provided the shortest distance?

  14. Distance, Rate, and Time Example 6: The following table displays rates and distances of Olympic swimmers. Which distance resulted in the shortest time?

  15. Distance, Rate, and Time Example 7: The following table shows 3 different rates for 3 members of the KBMS track team. Which rate had the shortest time?

  16. Distance, Rate, and Time • Example 8: A train traveled for ¾ hour at a speed of 80 miles per hour. It then immediately slowed to 60 miles per hour and traveled at that speed for the next ¼ hour. What is the total distance the train traveled during this hour? • Write your info down in a table. • Figure out what you need to find – total distance. • For part 1, d =rt. • d= (80 mph x 0.75 hr) 60 miles • For part 2, d =rt. • d = (60 mph x 0.25 hr) 15 miles • Add the distances together. • 60 miles + 15 miles = 75 miles

  17. Distance, Rate, and Time • Example 9: A car traveled for 1 hour at a speed of 25 miles per hour. It then immediately slowed to 10 miles per hour and traveled at that speed for the next ¾ hour. What is the total distance the car traveled during this hour? • Write your info down in a table. • Figure out what you need to find – total distance • For part 1, d =rt. • d= (25 mph x 1 hr) 25 miles • For part 2, d =rt. • d = (10 mph x 0.75 hr) 7.5 miles • Add the distances together. • 25 miles + 7.5 miles = 32.5 miles

  18. Distance, Rate, and Time Example 10: Tylesha and Jailene are traveling to a grizzlies game. On the way there, the girls leave Jailene’s house and Jailene’s mom travels at a speed of 35 miles per hour for ¼ hour. On the way back, she is caught in traffic and it takes 3/4 hour to get home. What was Jailene’s mom’s speed on the way home?

  19. Distance, Rate, and Time Example 11:The 8th graders took a plane to California for a class trip. On the trip there it flew 500 mph and on the return trip it went 480 mph. How long did the trip there take if the return trip took 7 hours?

  20. Distance, Rate, and Time Example 12: The staff travels downtown to a meeting for ½ hour at 75 mph. They return to KBM and it takes ¼ an hour. What is their speed on the trip home?

  21. Distance, Rate, and Time Example 13: The volleyball team travels to Cordova Middle for a game. On the way there they travel 10 miles at 45 mph. On the way back they travel 15 miles at 60 mph. How much total time did they spend on the bus?

  22. Distance, Rate, and Time Example 14: The choir’s trip to NY took 18 hours on the bus. They took the exact same route home and traveled at 70mph for 16.5 hours. What was the speed of the trip there?

  23. Distance, Rate, and Time Example 15: When Fed-Ex brought the Panda’s to Memphis it was a round trip flight. The trip there took 30 hours and the trip back took 38 hours. It averaged 550 mi/h on the return trip. Find the average speed of the trip there.

  24. Exit Ticket Each of you will complete your exit ticket on a note card. You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. You must work SILENTLY and INDEPENDENTLY. HOMEWORK – Worksheet

  25. Exit Ticket A train traveled for 14 at a speed of 65 miles per hour. It then sped up to 80 miles per hour and continued at that speed for 34 hour. What is the total distance the train traveled in that hour? Henry is practicing for a swim meet. 4 of his practice results are in the table below. For which distance did he swim the fastest?

  26. Do Now – (5 x 2), (√4) Please get out your notes and respond to the following SILENTLY & INDEPENDENTLY: An aircraft carrier made a trip to Guam and back. The trip there took three hours and the trip back took four hours. It averaged 6 km/h on the return trip. Find the average speed of the trip there.

  27. Today’s Agenda Do Now – 5 minutes Average Rate Equation – 5 minutes Average Rate INM – 10 minutes Guided Practice– 15 minutes Independent Practice – 10 minutes Exit Ticket – 5 minutes

  28. Today’s Objective SWBAT solve average rate distance, rate, and time problems.

  29. Average Rate/Speed Problems These problems are a little more complicated. In order to understand them, you must first think about what the problem is asking. The best way to solve these problems would be to make a table containing all the information given in the problem. The easiest way to do this is to make your columns distance, rate, and time, and your rows will represent each part of the trip. The average rate is ALWAYS the total distance divided by the total time.

  30. Average Rate/Speed Problems Here is an example of what your table would look like:

  31. Average Rate/Speed Problems • Example 1:Beyonce rode bicycle 2.2 miles up a hill in 0.2 hour. Then she rode back downhill on the same path in 0.12 hour. What is her average rate for the combined trip? • Fill in your table with the given information. MAKE YOUR OWN! • We know the distances are the same because it is a round trip. • Find the total distance. • Way there = 2.2 miles • Way back = 2.2 miles • 2.2 + 2.2 = 4.4 miles • Find the total time. • Way there = 0.2 hour • Way back = 0.12 hour • 0.2 + 0.12 = 0.32 hour • Divide the total distance by the total time to determine the average rate. • Average rate = 4.4 miles/ 0.32 hour • Average rate = 13.75 mph

  32. Average Rate/Speed Problems • Example 2: The principal traveled the following on her way to a conference: • 30 miles at 60 mph • 270 miles at 80 mph • ½ hour lunch and bathroom break • 550 miles at 50 mph What was her average speed, including lunch break? • Fill in your table with the given information. • Determine the time using d=rt. • Part 1: 30 mi = (60mph) xt • 30 mi / 60mph = 0.5 hr • Part 2: • Part 3: • Part 4: • Determine the total time. • Determine the total distance. • Divide the total distance by the total time to determine the average rate. • Average rate =

  33. Average Rate/Speed Problems Work on this with your partner. Example 3:

  34. Average Rate/Speed Problems Example 4: Junior ran at Shelby Farms 6.7 miles for 1.2 hours. Then he ran back on the same path in .9 hours. What is the average rate for his trip?

  35. Average Rate/Speed Problems • Example 5: The 8th grade trip consisted of the following: • Drive 300 miles for 65 mph • Stop for a bathroom break and dinner for 1 hour • Drive 200 miles for 4 hours. • Drive 150 miles at 55mph. • What was the average speed of the trip?

  36. Average Rate/Speed Problems • Example 6: Ms. Misconish traveled to St. Louis this weekend. Her trip is as follows: • Drive 120 miles at 70 mph. • Drive 65 miles at 60 mphs. • Stop for lunch for 15 minutes. • Drive 250 miles at 60 mph. • What was the average speed of the trip?

  37. Exit Ticket Each of you will complete your exit ticket on a note card. You will complete the exit ticket in 5 minutes and it must be turned in before you can exit the classroom. You must work SILENTLY and INDEPENDENTLY. HOMEWORK – Worksheet

  38. Exit Ticket • Vicki rode her bicycle 2.6 miles an hour up a hill in 0.24 hour. Then she rode back down the hill in 0.18 hour. What was her average rate for the combined trip? • The distances and speeds Tyrek drove during a trip are listed below: • He drove 20 miles at 50 miles per hour • He drove 120 miles at 65 miles per hour • He stopped for lunch for 1 hour • He drove 150 miles at 70 miles per hour • What was his average (mean) speed for his entire trip, including the time he stopped for lunch?

  39. Do Now – ( 20/2), (√9) • Please get out your notes and respond to the following SILENTLY & INDEPENDENTLY: • The distances and speeds the basketball team drove during a trip are listed below: • Drove 10 miles at 35 miles per hour • Drove 12 miles at 15 miles per hour • They stopped for lunch for 45 minutes • Drove 25 miles at 70 miles per hour • What was their average (mean) speed for their entire trip, including the time they stopped for lunch?

  40. Copy the following answers in ANY order on your BINGO card. You have 3 minutes. • 48.42 mph • 1.28 x 10-8 • 3 miles • 3.456 x 10-1 • 2.34 x 10-10 • 3.64 x 10-3 • 58.75 miles • 4.4 x 1012 • 4.14 x 10-2 • 0.3 hr/18 min • 1.7 x 10-2 • 8 x 10-6 • 8.3 x 1018 (rounded) • 53 mph • 2.1 x 10-7 • 0.00006547 • 7.14 x 107 • 1,710 miles • 8.75 x 1034 • 1 x 107 sec • 2.3825 x 10-5 • 150 km/hr • Printer, construction, poster, cardstock • 2007, 2010, 2008, 2009 • 3.2 x 107 • 2,540,000 • 2.7 x 10-6 • 7.2 mph • 2.3 x 10-6 • 4.1976 x 1011

  41. BINGO! Together, we will all work the problems. After we have worked a problem, you will get a chance to mark it off your bingo sheet. We will race each other to see who gets a bingo first!

  42. Do Now – (62 – 22), (√25) Please clear off your desk of everything except a pencil, calculator, and a plain sheet of paper (to cover your test with). The longer it takes you to complete this, the less time you will have for your test.

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