165 1.6 OtherTypes of Equations and Applications Solve each problem. See Example 3. 37. Painting a House (This problem appears in the 1994 movie Little Big League.) If Joe can paint a house in 3 hr, and Sam can paint the same house in 5 hr, how long does it take them to do it together? 38. Painting a House Repeat Exercise 37, but assume that Joe takes 6 hr working alone and Sam takes 8 hr working alone. 39. Pollution in a River Two chemical plants are polluting a river. If plant A produces a predetermined maximum amount of pollutant twice as fast as plant B, and together they produce the maximum pollutant in 26 hr, how long will it take plant B alone? Solve each equation. See Examples 4–6. 45. x - 22x + 3 = 0 46. x - 23x + 18 = 0 47. 23x + 7 = 3x + 5 48. 24x + 13 = 2x - 1 49. 24x + 5 - 6 = 2x - 11 50. 26x + 7 - 9 = x - 7 40. Filling a Settling Pond A sewage treatment plant has two inlet pipes to its settling pond. One pipe can fill the pond 3 times as fast as the other pipe, and together they can fill the pond in 12 hr. How long will it take the faster pipe to fill the pond alone? x represents the number of hours it takes plant A, working alone, to produce the maximum pollutant. Rate Time Part of Job Completed Pollution from A 1 x 26 26A 1 xB Pollution from B 26 Rate Time Part of Job Completed Faster Inlet Pipe 1 x 12 Slower Inlet Pipe 1 3x 12 x represents the number of hours it takes the faster inlet pipe, working alone, to fill the settling pond. 41. Filling a Pool An inlet pipe can fill Blake’s pool in 5 hr, and an outlet pipe can empty it in 8 hr. In his haste to surf the Internet, Blake left both pipes open. How long did it take to fill the pool? 42. Filling a Pool Suppose Blake discovered his error (see Exercise 41) after an hourlong surf. If he then closed the outlet pipe, how much more time would be needed to fill the pool? 43. Filling a Sink With both taps open, Robert can fill his kitchen sink in 5 min. When full, the sink drains in 10 min. How long will it take to fill the sink if Robert forgets to put in the stopper? 44. Filling a Sink If Robert (see Exercise 43) remembers to put in the stopper after 1 min, how much longer will it take to fill the sink?
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