38. Teamwork You can stuff envelopes twice as fast as your friend. Together, you can stuff 6750 envelopes in 4.5 hours. How long would it take each of you working alone to complete the job?
39. Grades On the first four tests of the term your average is 84%. You think you can score 96% on each of the remaining tests. How many consecutive test scores of 96% would you need to bring your average up to 90% for the term?
40. Error Analysis Describe and correct the error made in solving the equation.
41. Fuel Economy Suppose you drive an average of 15,000 miles per year, and your car gets 24 miles per gallon. Suppose gasoline costs $3.60 a gallon.
    1. How much money do you spend each year on gasoline?
    2. You plan to trade in your car for one that gets x more miles per gallon. Write an expression to represent the new yearly cost of gasoline.
    3. Write an expression to represent your total savings on gasoline per year.

    4. Suppose you can save $600 a year with the new car. How many miles per gallon does the new car get?

       
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42. Woodworking A tapered cylinder is made by decreasing the radius of a rod continuously as you move from one end to the other. The rate at which it tapers is the taper per foot. You can calculate the taper per foot using the formula T = 24 ( R − r ) L . t equals . fraction 24 . open , r minus r , close , over l end fraction . .

    The lengths R, r, and L are measured in inches.

    

    1. Solve this equation for L.
    2. What is L for T = 0.75 , t equals , 0.75 , comma  0.85, and 0.95, if R = 4  in  . ; r = 3  in  . ? r equals 4 , in , . semicolon r equals 3 , in , . question mark

Solve each equation. Check each solution.

43. 15 x + 9 x − 7 x + 2 = 9 15 over x , plus . fraction 9 x minus 7 , over x plus 2 end fraction . equals 9
44. 2 x + 2 − 1 x = − 4 x ( x + 2 ) fraction 2 , over x plus 2 end fraction . minus , 1 over x , equals . fraction negative 4 , over x . open , x plus 2 , close end fraction
45. 1 b + 1 + 1 b − 1 = 2 b 2 − 1 fraction 1 , over b plus 1 end fraction . plus . fraction 1 , over b minus 1 end fraction . equals . fraction 2 , over b squared , minus 1 end fraction
46. c − c 3 + c 5 = 26 c minus , c over 3 , plus , c over 5 , equals 26
47. 1 x − 5 = x x 2 − 25 fraction 1 , over x minus 5 end fraction . equals . fraction x , over x squared , minus 25 end fraction
48. k k + 1 + k k − 2 = 2 fraction k , over k plus 1 end fraction . plus . fraction k , over k minus 2 end fraction . equals 2
49. 5 x 2 − 7 x + 12 − 2 3 − x = 5 x − 4 fraction 5 , over x squared , minus 7 x plus 12 end fraction . minus . fraction 2 , over 3 minus x end fraction . equals . fraction 5 , over x minus 4 end fraction
50. 10 2 y + 8 − 7 y + 8 y 2 − 16 = − 8 2 y − 8 fraction 10 , over 2 y plus 8 end fraction . minus . fraction 7 y plus 8 , over y squared , minus 16 end fraction . equals . fraction negative 8 , over 2 y minus 8 end fraction
51. 7 x + 3 x 2 − 8 x + 15 + 3 x x − 5 = 1 3 − x fraction 7 x plus 3 , over x squared , minus 8 x plus 15 end fraction . plus . fraction 3 x , over x minus 5 end fraction . equals . fraction 1 , over 3 minus x end fraction
52. 2 x + 3 − 3 4 − x = 2 x − 2 x 2 − x − 12 fraction 2 , over x plus 3 end fraction . minus . fraction 3 , over 4 minus x end fraction . equals . fraction 2 x minus 2 , over x squared , minus x minus 12 end fraction
53. Writing Write and solve a problem that can be modeled by a rational equation.

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