1. Warm–up #4 1. Suppose 42 nickels, dimes, & quarters are worth $4.80 & there are twice as many quarters as dimes. How many of each are there? Amount$/eaTotal Nickels Dimes Quarters Total.25(2x) 0.05 2x x 42 – x – 2x 0.10 0.25.05(42 – 3x).10(x).05(42 – 3x) +.10(x) +.25(2x) = 4.80 = 42 4.80

2. Warm – up #4 cont’d.05(42 – 3x) +.10(x) +.25(2x) = 4.80 5(42 – 3x) + 10(x) + 25(2x) = 480 210 – 15x +10x + 50x = 480 45x = 270 x = 6 2x = 12 42 – x – 2x = 24 24 Nickels, 6 Dimes, & 12 Quarters

3. Homework Log Wed 10/7 Lesson 2 – 2 Learning Objective: To solve coin & distance problems Hw: #205 Pg. 111 #15, 16, 27 – 32 all & RE-DO 6, 23

4. 10/7/15 Lesson 2 – 2 Coin & Distance Problems Day 3 Advanced Math/Trig

5. Learning Objective To solve coin problems To solve distance problems

6. Distance Problem 1. Sue drove her boat upstream in 5.5 hours & then made the return trip downstream in 4.5 hours. During both trips, the boat was running at a rate of 20 mph in still water. Find the rate of the current. RateTimeDistance Upstream Downstream 5.5 20 + c 20 – c 4.5 5.5(20 – c) 4.5(20 + c) upstream = still rate – current downstream = still rate + current 5.5(20 – c) = 4.5(20 + c) = Dist is = against flow with flow

7. Distance Problem #1 Cont’d 5.5(20 – c) = 4.5(20 + c) 110 – 5.5c = 90 + 4.5c 20 = 10c 2 = c Rate of current = 2 mph

8. Distance Problem 2. A train left Los Al and traveled north at 70 mph. Two hours later, another train left Fullerton and traveled south at 90 mph. How many hours had the first train traveled when they were 1420 miles apart? RateTimeDistance Train 1 Train 2 Total x 90 70 x – 2 70x 90(x – 2) 70x + 90(x – 2) = 1420 = 1420 2 hrs later  it took 2 hrs less time

9. 70x + 90(x – 2) = 1420 70x + 90x – 180 = 1420 160x = 1600 x = 10 1 st train traveled 10 hours Distance Problem #2 Cont’d

10. Distance Problem 3. Jenny left the movie theater and drove west. One hour later, Trev left the theater driving 20 mph faster in an effort to catch up to her. After three hours. Trev finally caught up. Find Jenny’s avg speed RateTimeDistance Jenny Trev Total 4 x + 20 x 3 4x 3(x + 20) 4x = 3(x + 20) = SAME! 60 mph Trev caught up to Jenny, so they went the same distance!

11. Distance Problem 4. Nick left school and drove north at 20 mph. Paul left school some time later and drove south at 70 mph. After Nick had driven for 4 hours, they were 290 miles apart. How long had Paul been driving? RateTimeDistance Nick Paul Total 4 70 20 x 80 70x 80 + 70x = 290 = 290 3 hours

12. Distance Problem 5. Shawna made a trip to the recycling plant and back. The trip there took 3 hours and the trip back took 4 hours. What was Shawna’s avg speed on the trip there if she avg 30 mph on the return trip? RateTimeDistance There Return Total 3 30 x 4 3x 120 3x = 120 = SAME! 40 mph Roundtrip = same distance there and back!

13. Ticket Out the Door It took a plane 5.5 hours to fly from LA to NY with a 60 mph tailwind. It took the plane 6 hours to fly back with the same headwind. What was the plane’s still air speed?

14. Homework #205 Pg. 111 15, 16, 27 – 32 all & RE-DO 6, 23