1. Any questions on the Section 6.5 homework?

2. Section 6.6 Rational Expressions and Problem Solving

3. Now please CLOSE YOUR LAPTOPS and turn off and put away your cell phones. Sample Problems Page Link (Dr. Bruce Johnston )

4. NOTE: Make sure you turn in the worksheet for this assignment showing all your work. If you don’t turn this in, your online score will be reduced. If you don’t completely show your work on any problem/s, your online score will be reduced for those problems.

5. Ratios & Rates A ratio is the quotient of two numbers or two quantities. The units associated with the ratio are important. The units should match. If the units do not match, it is called a rate, rather than a ratio. The ratio of the numbers a and b can also be written as a:b, or.

6. A proportion is two ratios (or rates) that are equal to each other. We can rewrite the proportion by multiplying by the LCD, bd. This simplifies the proportion to ad = bc. This is commonly referred to as the cross product.

7. Solve the proportion for x. Example

8. Example (cont.) true Substitute the value for x into the original equation, to check the solution. So the solution is ALWAYS CHECK YOUR ANSWER!!!

9. If a 170-pound person weighs approximately 65 pounds on Mars, how much does a 9000- pound satellite weigh on Mars? Example Solution: Let x = satellite’s weight on Mars. Then our proportion is 170 = 9000 65 x Now cross multiply:

10. This section involves applied problems that can be modeled by rational equations. The techniques from the previous section can be used to solve these equations. It is especially important that you check your possible answers, in order to verify that they make sense in the applied problems.

11. The quotient of a number and 9 times its reciprocal is 1. Find the number. Example Understand Read and reread the problem. If we let n = the number, then = the reciprocal of the number

12. Example (cont.) Translate The quotient of  a number n and 9 times its reciprocal is = 1 1

13. Example (cont.) Solve

14. Example (cont.) Interpret Check: We substitute the values we found from the equation back into the problem. Note that nothing in the problem indicates that we are restricted to positive values. State: The missing number is 3 or –3. true ALWAYS CHECK YOUR ANSWER!!!

15. An experienced roofer can roof a house in 26 hours. A beginner needs 39 hours to do the same job. How long will it take if the two roofers work together? Example

16. Example (cont.) Understand Experienced roofer 26 1/26 Beginning roofer 39 1/39 Together t 1/t Time in hrs Portion of job/hr Read and reread the problem. By using the times for each roofer to complete the job alone, we can figure out their corresponding work rates in terms of the portion of the job done per hour.

17. Example (cont.) Translate Since the rate of the two roofers working together would be equal to the sum of the rates of the two roofers working independently,

18. Example (cont.) Solve

19. Example (cont.) Interpret Check: We substitute the value we found from the proportion calculation back into the problem. true State: The roofers would take 15.6 hours working together to finish the job. ALWAYS CHECK YOUR ANSWER!!!

20. The speed of Lazy River’s current is 5 mph. A boat travels 20 miles downstream in the same time as traveling 10 miles upstream. Find the speed of the boat in still water. Example

21. Example (cont.) Understand Read and reread the problem. By using the formula d=rt, we can rewrite the formula to find that t = d/r. We note that the rate of the boat downstream would be (the rate in still water) + (the water current) and the rate of the boat upstream would be (the rate in still water) – (the water current.) Down 20 r+5 20/(r+5) Up 10 r-5 10/(r-5) Dist rate time = d/r

22. Example (cont.) Translate Since the problem states that the time to travel downstream was the same as the time to travel upstream, we get the equation

23. Solve Example (cont.)

24. Interpret Check: We substitute the value we found from the proportion calculation back into the problem. true State: The speed of the boat in still water is 15 mph. ALWAYS CHECK YOUR ANSWER!!!

25. Word Problems involving Rational Equations Example we just did in class: The quotient of a number and 9 times its reciprocal is 1. Find the number. Homework problem with similar solution method:

26. Proportion Problems

27. Work Problems Time in hoursPortion of job per hour Worker 1 Worker 2 Together Example we just did in class: Homework problem with similar solution method:

28. Distance = Rate x Time DistanceRateTime Down Up Example we just did in class: Homework problem with similar solution method:

29. Reminder: This homework assignment on section 6.6 is due at the start of next class period. The required paper worksheet for this assignment MUST be turned in by the start of the next class session or your online score will be reduced.

30. You may now OPEN your LAPTOPS and begin working on the homework assignment.