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Quadratic Equations in Distance Problems Practice Problems (page 2)

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Set 2: Traveling at Right Angles

To review problems where you need to find the distance between two bodies traveling at right angles away from each other, go to Quadratic Equations in Distance Problems Help

Practice

1. A car and plane leave an airport at the same time. The car travels eastward at an average speed of 45 mph. The plane travels southward at an average speed of 200 mph. After how long will they be 164 miles apart?
2. Two joggers begin jogging from the same point. One jogs south at the rate of 8 mph and the other jogs east at a rate of 6 mph. When will they be five miles apart?
3. A cross-country cyclist crosses a railroad track just after a train passed. The train is traveling southward at an average speed of 60 mph. The cyclist is traveling westward at an average speed of 11 mph. When will they be 244 miles apart?
4. A motor scooter and a car left a parking lot at the same time. The motor scooter traveled north at 24 mph. The car traveled west at 45 mph. How long did it take for the scooter and car to be 34 miles apart?
5. Two cars pass each other at 4:00 at an overpass. One car is headed north at an average speed of 60 mph and the other is headed east at an average speed of 50 mph. At what time will the cars be 104 miles apart? Give your solution to the nearest minute.

Solutions

1. Let t represent the number of hours each has traveled. The plane’s distance after t hours is 200t and the car’s distance is 45 t .

The car and plane will be 164 miles apart after 0.80 hours or 48 minutes.

2. Let t represent the number of hours after the joggers began jogging. The distance covered by the southbound jogger after t hours is 8t, and the distance covered by the eastbound jogger is 6 t .

The joggers will be five miles apart after hour or 30 minutes.

3. Let t represent the number of hours after the cyclist crosses the track. The distance traveled by the bicycle after t hours is 11 t and the distance traveled by the train is 60 t .

After four hours the cyclist and train will be 244 miles apart.

4. Let t represent the number of hours after the scooter and car left the parking lot. The car’s distance after t hours is 45 t . The scooter’s distance is 24 t .

The car and scooter will be 34 miles apart after of an hour or 40 minutes.

5. Let t represent the number of hours after the cars passed the overpass. The northbound car’s distance after t hours is 60 t and the eastbound car’s distance is 50 t .

The cars will be 104 miles apart after about 1.33 hours or 1 hour 20 minutes. The time will be about 5:20.

Set 3: Round Trips with Different Average Speeds

To review distance problems where people are making a round trip, go to Quadratic Equations in Distance Problems Help

Practice

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 0.2 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 Buffalo, 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 Buffalo? (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 traffic 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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