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11r 6 0 (This does not lead to a solution)
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The jogger s average speed to the park was 5 1 6 mph
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1 A man rode his bike six miles to work The wind reduced his average speed on the way home by 2 mph The round trip took 1 hour 21 minutes How fast was he riding on the way to work 2 On a road trip a saleswoman traveled 120 miles to visit a customer She averaged 15 mph faster to the customer than on the return trip She spent a total of 4 hours 40 minutes driving What was her average speed on the return trip 3 A couple walked on the beach from their house to a public beach four miles away They walked 02 mph faster on the way home than on the way to the public beach They walked for a total of 2 hours 35 minutes How fast did they walk home 4 A family drove from Detroit to Bu alo, a distance of 215 miles, for the weekend They averaged 10 mph faster on the return trip They spent a total of seven hours on the road What was their average speed on the trip from Detroit to Bu alo (Give your solution accurate to one decimal place) 5 Boston and New York are 190 miles apart A professor drove from his home in Boston to a conference in New York On the return trip, he faced heavy tra c and averaged 17 mph slower than on his way to New York He spent a total of 8 hours 5 minutes on the road How long did his trip from Boston to New York last
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1 Let r represent the man s average speed on the way to work Then r 2 represents the man s average speed on his way home The 6 distance each way is 6 miles, so the time he rode to work is , r 6 and the time he rode home is The total time is 1 hour 21 r 2
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7 minutes 1 21 1 20 27 60 20
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equation to solve is
hours
6 6 27 The LCD is 20r r 2 r r 2 20 6 6 27 20r r 2 20r r 2 20r r 2 r r 2 20 120 r 2 120r 27r r 2 120r 240 120r 27r2 54r 240r 240 27r2 54r 0 27r2 294r 240 1 1 0 27r2 294r 240 3 3 0 9r2 98r 80 0 r 10 9r 8 r 10 0 r 10 9r 8 0 (This does not lead to a valid solution)
The man s average speed on his way to work was 10 mph 2 Let r represent the saleswoman s average speed on her return trip Her average speed on the way to the customer is r 15 The distance each way is 120 miles She spent a total of 4 hours 40 minutes 4 40 4 2 14 hours driving The time spent driving to the 60 3 3 120 120 customer is The time spent driving on the return trip is r 15 r 120 120 14 The LCD is 3r r 15 The equation to solve is r 15 r 3 3r r 15 120 120 14 3r r 15 3r r 15 r 15 r 3 360r 360 r 15 14r r 15 360r 360r 5400 14r2 210r 720r 5400 14r2 210r 0 14r2 510r 5400 1 1 0 14r2 510r 5400 2 2 0 7r2 255r 2700
CHAPTER 11 Quadratic Applications
q 255 255 2 4 7 2700
2 7 p p 255 65,025 75,600 255 140,625 255 375 14 14 14   255 375 r 45 r is not a solution 14 The saleswoman averaged 45 mph on her return trip 3 Let r represent the couple s average rate on their way home, then r 0:2 represents the couple s average speed to the public beach The distance to the public beach is 4 miles They walked for a total 7 of 2 hours 35 minutes 2 35 2 12 31 hoursThe time spent walk60 12 4 4 ing to the public beach is The time spent walking home is r 0:2 r 4 4 31 The equation to solve is The LCD is 12r r 0:2 r 0:2 r 12 12r r 0:2 4 4 31 12r r 0:2 12r r 0:2 r 0:2 r 12 48r 48 r 0:2 31r r 0:2 48r 48r 9:6 31r2 6:2r 96r 9:6 31r2 6:2r 0 31r2 102:2r 9:6 (Multiplying by 10 to clear the decimals would result in fairly large numbers for the quadratic formula) q 102:2 102:2 2 4 31 9:6 r 2 31 p p 102:2 10,444:84 1190:4 102:2 9254:44 62 62   102:2 96:2 16 3 3 ; is not a solution 62 5 31 31 The couple walked home at the rate of
16 5
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