An Object That Moves at a Constant Rate Is Said to Be in Uniform Motion

An object that moves at a constant rate is said to be in uniform motion.

The formula gives the relationship between distance, rate , and time .

Uniform motion problems may involve objects going in the same direction, opposite directions, or round trips.

Draw a picture for each situation and fill in the blank.

1. When two objects are traveling in the SAME DIRECTION at different rates, then the distances the objects travel are the ______.

1. When two objects are moving in OPPOSITE DIRECTIONS, the ______of their distances is equal to the total distance.

1. For uniform motion problems that involve a ROUND TRIP, the distance going is ______to the distance returning.

I) SAME DIRECTION. Draw a picture.

a)A passenger train leaves a station at 1pm and travels at an average rate of 72mi/h. A high-speed train leaves the same station an hour later and travels at an average rate of 90mi/h. The trains follow the same route. In how many hours will the high-speed train overtake the passenger train?

b) A group of campers left a campsite in a canoe traveling at a speed of 10 km/h. Two hours later the group leader left the campsite in a motorboat traveling in the same direction at a speed of 22 km/h. How long did it take for the motorboat to catch up with the canoe?

c) Joe left home on his bicycle for a long-distance ride. Meredith left 3 hours later on her motorcycle carrying Joe’s lunch. Meredith traveled at 42 mph and she caught up to Joe in 1.5 hours. How fast was Joe traveling?

d)Suppose John and Gina leave at the same time traveling in the same direction. Gina drives at 85 mph and John at 70 mph. How long until they are 90 miles apart?

II)OPPOSITE DIRECTION Draw a picture.

1. Jane and Peter leave their home traveling in opposite directions on a straight road. Peter drives 15 mi/h faster than Jane. After 3 hours they are 225 miles apart. Find Peter’s and Jane’s rate.

1. Sarah and John leave New York City traveling in opposite directions. Sarah drives 12 mi/h faster than John. After 2 hours they are 176 miles apart. Find John’s and Sarah’s Speed.

1. Two trains leave Washington D.C. at the same time, one traveling north and the other south. The first train travels at 60 mph and the second at 55 mph. In how many hours will the trains be 805miles apart?

1. At the same time Mike leaves Union for Virginia Beach, Paul leaves Virginia Beach for Union. The distance between the two towns is 540 miles. Mike’s average speed is 15 mph faster than Paul’s. How fast is Paul driving if they pass each other in 4 hours?

III) ROUND TRIP

1. Noya travels into the city to buy software at the computer store. Because of the traffic, she averages only 15mi/h. On her drive home, she averages 35 mi/h. If the total drive time is 2 hours, how long did it take her to drive to the computer store?

1. On his way to work from home, Uncle Jack averaged only 20 mi/h. On his drive home from work, he averages 40 mi/h. If the total drive time was hours, how long did it take him to drive to work?

1. Cheryl is on her way home from work averaging a speed of 30mph. Once she gets home she remembered she left her purse at work. Because of traffic, she averages only 10mph going from home back to work. If the total drive time is 1.5 hours, how long does it take her to drive back to work?

1. On his way to the food store from home, Mike averages only 25 mph. On his drive home, he averages 55mph. If the total drive was 2 hours, how long did it take him to drive to the food store?

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