1. Interest, Mixture, Uniform Motion, Constant Rate Jobs
Section 1.6
Problem Solving;
Interest, Mixture, Uniform Motion, Constant Rate Jobs

3. OBJECTIVE 1

4. (a) For uniform motion, the time required for an object to travel equals the distance traveled divided by the velocity of the object.
t = d/v
(b) The length of a rectangle is four times its width.
l = 4w
(c) Five times a number, decreased by 3
5n - 3
(d) The product of 3 and a number increased by 5
3n + 5

5. OBJECTIVE 2

7. Suppose you borrow $1000 for 6 months at the simple interest rate of 6% per annum. What is the interest you will be charged on this loan? If you pay the loan back at the end of 6 months, what is the amount you must pay?
I = 1000(.06)(.5) = $30

8. Jennifer has $10,000 to invest and requires an overall rate of return of 8%. She can invest in a safe, government-insured certificate of deposit, but it only pays 7%. To obtain 8% she agrees to invest some of her money in noninsured corporate bonds paying 10%. How much should be placed in each investment to achieve her goal?
Let x = amount invested at 7%
Let y = amount invested at 10%
I = Prt = $800 = .07x + .10y and x + y = $10,000
y = $10,000 - x
800 = .07x + .10(10,000 – x)
x = $6, and y = $3,333.33

9. OBJECTIVE 3

10. Revenue = Number of Items Sold * Price Per Item
$7B A = 9 * 100 lbs where A + B =100
B = A
7(100-A) + 12A = 900
A + 12A = 900
5A = 200
A = 40
A grade = 40 lbs.
B grade = 60 lbs.

11. OBJECTIVE 4

13. Brad, who is a long-distance runner, runs at an average speed of 9 miles per hour. Three hours after Brad leaves his house, you leave in your Toyota and follow the same route. If your average speed is 45 mi/hr, how long will it be before you catch up to Brad? How far will each of you be from your home?
d = rt and let t be the time it takes for you to catch Brad
Brad’s distance: 9(t + 3) = 45t Your distance
9t + 27 = 45t
36t = 27
t = ¾ hour and distance travel is 45(3/4) = miles

15. OBJECTIVE 5

16. Janice can paint a fence in 6 hours
Janice can paint a fence in 6 hours. If she has her son Mike help her, they can get the fence done in 4 hours. How long would Mike take to paint the fence if he worked alone?
Janice’s per unit of work: 1/6
Mike’s per unit of work: 1/t
1/6 + 1/t = ¼
2t + 12 = 3t
t = 12 hours