268 Chapter 3 Systems of Linear Equations and Inequalities 25. A plane flies from Atlanta to Los Angeles against the wind in 5 hr.The return trip back to Atlanta with the wind takes only 4 hr. If the distance between Atlanta and Los Angeles is 3200 km, find the speed of the plane in still air and the speed of the wind. 26. The Gulf Stream is a warm ocean current that 13 extends from the eastern side of the Gulf of Mexico up through the Florida Straits and along the southeastern coast of the United States to Cape Hatteras, North Carolina. A boat travels with the current 100 mi from Miami, Florida, to Freeport, Bahamas, in 2.5 hr.The return trip against the same current takes 3hr. Find the speed of the boat in still water and the speed of the current. 27. A moving sidewalk in the Atlanta airport moves people between gates. It takes Molly’s 8-year-old son Stephen 20 sec to travel 100 ft walking with the sidewalk. It takes him 30 sec to travel 60 ft walking against the moving sidewalk (in the opposite direction). Find the speed of the moving sidewalk and Stephen’s walking speed on nonmoving ground. 28. Kim rides a total of 48 km in the bicycle portion of a triathlon.The course is an “out and back” route. It takes her 3 hr on the way out against the wind.The ride back takes her 2 hr with the wind. Find the speed of the wind and Kim’s speed riding her bike in still air. Concept 5: Applications Involving Geometry For Exercises 29–34, solve the applications involving geometry. If necessary, refer to the geometry formulas listed in the inside back cover of the text. 29. In a right triangle, one acute angle measures 6 more than 3 times the other. If the sum of the measures of the two acute angles must equal 90, find the measures of the acute angles. (See Example 5.) 30. An isosceles triangle has two angles of the same measure. If the angle represented by y measures 3 less than the angle x, find the measures of all angles of the triangle. y x 31. Two angles are supplementary. One angle measures 2 less than 3 times the other.What are the measures of the two angles? y x x 32. The measure of one angle is 5 times the measure of another. If the two angles are supplementary, find the measures of the angles. 33. One angle measures 6 more than twice another. If the two angles are complementary, find the measures of the angles. 34. Two angles are complementary. One angle measures 15° more than 2 times the measure of the other.What are the measures of the two angles? Mixed Exercises 35. How much pure gold (24K) must be mixed with 60% gold to get 20 grams (g) of 75% gold? 36. Connie is the head of maintenance at a large hospital. She received news of a new state mandate indicating that the minimum strength for disinfectant was to be 17%, up from the old requirement of 15%. Connie had plenty of barrels of 15% disinfectant left over, and also lots of the strong 55% disinfectant used in rooms for patients with highly contagious diseases. How many gallons of each disinfectant should be mixed to get 50 gal of 17% disinfectant?
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