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2. One antifreeze solution is 20% alcohol. Another antifreeze solution is 12% alcohol. How many liters of each solution should be combined to make 15 L of antifreeze solution that is 18% alcohol?

Problem 3 Solving a Wind or Current Problem

Travel A traveler flies from Charlotte, North Carolina, to Los Angeles, California. At the same time, another traveler flies from Los Angeles to Charlotte. The air speed of each plane is the same. The ground speeds are shown below. What is the air speed? What is the wind speed?

Use the ground speed with the tailwind and with the headwind to write the system. Let a =  the air speed of the planes  . eh equals . theairspeedoftheplanes . .  Let w =  the wind speed  . w equals . thewindspeed . .

air   speed + wind   speed = ground speed with tailwind a + w = 550   air   speed − wind   speed = ground speed with headwind a − w = 495 table with 1 row and 3 columns , row1 column 1 , table with 2 rows and 5 columns , row1 column 1 , air , speed , column 2 plus , column 3 wind , , speed , column 4 equals , column 5 table with 2 rows and 1 column , row1 column 1 , groundspeed , row2 column 1 , withtailwind , end table , row2 column 1 , eh , column 2 plus , column 3 w , column 4 equals , column 5 550 , end table , column 2 , column 3 table with 2 rows and 5 columns , row1 column 1 , air , speed , column 2 minus , column 3 wind , , speed , column 4 equals , column 5 table with 2 rows and 1 column , row1 column 1 , groundspeed , row2 column 1 , withheadwind , end table , row2 column 1 , eh , column 2 minus , column 3 w , column 4 equals , column 5 495 , end table , end table

Choose a method to solve the system. Use elimination.

a + w = 550 a − w = 495 _   2 a + 0 = 1045 a = 522.5 Add the equations . Solve for  a . table with 2 rows and 2 columns , row1 column 1 , modified table with 2 rows and 2 columns , row1 column 1 , eh plus w , column 2 equals 550 , row2 column 1 , eh minus w , column 2 equals 495 , end table with under bar below , column 2 , row2 column 1 , table with 2 rows and 2 columns , row1 column 1 , 2 eh plus 0 , column 2 equals , 1045 , row2 column 1 , eh , column 2 equals , 522.5 , end table , column 2 table with 2 rows and 1 column , row1 column 1 , cap addtheequations . . , row2 column 1 , cap solvefor . eh . , end table , end table

Substitute 522.5 for a in either equation and solve for w.

522.5 + w = 550 Substitute  522.5  for a in the first equation . w = 27.5 Solve for  w . table with 2 rows and 3 columns , row1 column 1 , 522.5 , plus w , column 2 equals 550 , column 3 cap substitute . 522.5 . forainthefirstequation . . , row2 column 1 , w , column 2 equals , 27.5 , column 3 cap solvefor . w . , end table

The air speed is 522.5 mi/h. The wind speed is 27.5 mi/h.