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# Quadratic Equations in Distance Problems Practice Problems (page 3)

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By — McGraw-Hill Professional
Updated on Sep 27, 2011

#### Solutions

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 distance each way is 6 miles, so the time he rode to work is , and the time he rode home is . The total time is 1 hour 21 minutes = hours. The equation to solve is . The LCD is 20 r (r – 2).

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 hours driving. The time spent driving to the customer is . The time spent driving on the return trip is . The equation to solve is . The LCD is 3 r ( r + 15).

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 of 2 hours 35 minutes = hours. The time spent walking to the public beach is . The time spent walking home is . The equation to solve is . The LCD is 12 r ( r – 0.2).

(Multiplying by 10 to clear the decimals would result in fairly large numbers for the quadratic formula.)

The couple walked home at the rate of mph.

4. Let r represent the average speed from Detroit to Buffalo. The average speed from Buffalo to Detroit is r + 10. The distance from Detroit to Buffalo is 215 miles and the total time the family spent driving is 7 hours. The time spent driving from Detroit to Buffalo is . The time spent driving from Buffalo to Detroit is . The equation to solve is . The LCD is r ( r + 10).

The family averaged 56.8 mph from Detroit to Buffalo.

5. Let r represent the average speed on his trip from Boston to New York. Because his average speed was 17 mph slower on his return trip, r – 17 represents his average speed on his trip from New York to Boston. The distance between Boston and New York is 190 miles. The time on the road from Boston to New York is and the time on the road from New York to Boston is . The time on the road from Boston to New York plus the time on the road from New York to Boston is 8 hours 5 minutes hours. The equation to solve is . The LCD is 12 r ( r –17).

The rate cannot be because the total round trip is only 8 hours 5 minutes. The professor’s average speed from Boston to New York is 57 mph. We want his time on the road from Boston to New York. His time on the road from Boston to New York is hours or 3 hours 20 minutes.

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