59. Filling a fountain. Pete’s fountain can be filled using a pipe or a hose. The fountain can be filled using the pipe in 6 hours or the hose in 12 hours. How long will it take to fill the fountain using both the pipe and the hose? 60. Mowing a lawn. Albert can mow a lawn in 40 minutes, while his cousin Vinnie can mow the same lawn in one hour. How long would it take to mow the lawn if Albert and Vinnie work together? 61. Printing a report. Debra plans to use two computers to print all of the copies of the annual report that are needed for the year-end meeting. The new computer can do the whole job in 2 hours while the old computer can do the whole job in 3 hours. How long will it take to get the job done using both computers simultaneously? 62. Installing a dishwasher. A plumber can install a dishwasher in 50 min. If the plumber brings his apprentice to help, the job takes 40 minutes. How long would it take the apprentice working alone to install the dishwasher? 63. Filling a tub. Using the hot and cold water faucets together, a bathtub fills in 8 minutes. Using the hot water faucet alone, the tub fills in 12 minutes. How long does it take to fill the tub using only the cold water faucet? 64. Filling a tank. A water tank has an inlet pipe and a drain pipe. A full tank can be emptied in 30 minutes if the drain is opened and an empty tank can be filled in 45 minutes with the inlet pipe opened. If both pipes are accidentally opened when the tank is full, then how long will it take to empty the tank?
6-67 Chapter 6 Summary 447 Wrap-Up± 6 Examples x 1 ( x � 3) x 3 x 1 y x 3 8 x + 2 2(4 x + 1) 4 x + 1 4 x 2(2 x ) 2 x 7 2 x x 1 2 x 5 5 3 x x x Examples 3 6 18 x 3 x 5 x 8 a 5 a x 9 ax 6 x 3 x 9 x 3 5 5 Examples 8, 12 LCD 24 4 ab 3 , 6 a 2 b 4 ab 3 2 2 ab 3 6 a 2 b 2 3 a 2 b 2 b 3 2 b 3 LCD 2 2 3 a 12 a 2 x 7 x 9 x + x 3 x 3 x 3 2 1 6 1 7 + + x 3 x 3 x 3 x 3 x Summary Rational Expressions Rational expression Rational Function Rule for reducing rational expressions Least common denominator Finding the least common denominator Addition and subtraction of rational expressions The ratio of two polynomials with the denominator not equal to 0 If a rational expression is used to determine y from x , then y is a rational function of x . If a � 0 and c � 0, then ab b . ac c (Divide out the common factors.) Multiplication and Division of Rational Expressions Multiplication If b � 0 and d � 0, then a b d c b a d c . Division If b � 0, c � 0, and d � 0, then a b (Invert the divisor and multiply.) d c a b d c . Addition and Subtraction of Rational Expressions The LCD of a group of denominators is the smallest number that is a multiple of all of them. 1. Factor each denominator completely. Use exponent notation for repeated factors. 2. Write the product of all of the different factors that appear in the denominators. 3. On each factor, use the highest power that appears on that factor in any of the denominators.
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