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

OBJECTIVE 1

(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

OBJECTIVE 2

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  

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 = $6,666.67 and y = $3,333.33

OBJECTIVE 3

Revenue = Number of Items Sold * Price Per Item $7B + 12A = 9 * 100 lbs where A + B =100 B = 100 - A 7(100-A) + 12A = 900 700 - 7A + 12A = 900 5A = 200 A = 40 A grade = 40 lbs. B grade = 60 lbs.

OBJECTIVE 4

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) = 33.75 miles

OBJECTIVE 5

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