Uniform Motion problems

Example 1 – (motion in the same direction)

Two cars heading for Pittsburgh on the Pennsylvania Turnpike left a service area at the same time. Their average speeds differed by 15 miles per hour. Three hours later the faster car reached the Pittsburgh interchange, and the other car reached the interchange an hour after that. Find the average speed of each car.

Example #2. (motion in opposite directions)

A fishing trawler radioed the Coast Guard for a helicopter to pick up an injured crewman. At the time, the helicopter left the Coast Guard station, the trawler was 356 nautical miles away and heading directly toward the station. If the average speed of the trawler was 18 knots (nautical miles per hour) and that of the helicopter was 160 knots, how long did it take the helicopter to reach the trawler?

Example #3 (roundtrip)

Using the butterfly stroke to swim the length of the pool, Eva averaged 1.5 meters per second. Swimming back, she used the breast stroke and average 1.2 meters per second. The entire swim took 1 minute and 15 seconds. How long was the pool?

1. A jet airplane and a light plane left the same airport at the same time and flew in the same direction. Flying 350 m.p.h. faster than the light plane, the jet passed over Miller Field 1 hour after takeoff. Two hours later, the light plane landed at Miller Field. What were the average speed of the planes?

2. Miss Joshi drove a car for 2 hours at 45 m.p.h. to get to O’Hare Airport. She then took and airplane to Dallas, Flying for 2 hours. If the total distance traveled was 885 miles, what was the average speed of the airplane?

3. Heading due south at a steady rate of 3 m.p.h., a dog sled left the Chinook trading post at 8 a.m. A second sled left the post at the same time, but traveled due north at 4 m.p.h. When were the sleds 28 miles apart?

4. The Queen Elizabeth II cruising due west at 28 knots, passed a container ship, sailing due east at 22 knots. How long after passing each other were the ships 250 nautical miles apart?

5. A motorist driving 75 m.p.h. is chased by a state trooper going 90 m.p.h. If the motorist is 3 miles ahead of the trooper, how long will it take for the trooper to overtake the motorist?

6. A bus, going 40 m.p.h. left the Wells City terminal @ 9:00 a.m. Another bus on the same route left ½ hour later. If the second bus caught up to the first one at 11:30 that day, how fast was the 2^nd bus traveling?

7. From the bottom of a toboggan run, a chair lift carried Ida to the top at the rate of 120 feet per minute. She rode her toboggan down the run at an average speed of 2280 feet per minute. How long was the run if the round trip time was 30 minutes?

8. Running at an average rate of 400 meters per minute, an athlete dashed to the end of a course and then walked back to her starting point at an average rate of 80 meters per minute. How long was the course if it took her 6 minutes to make the dash and the walk back?

9. A forest service helicopter on a fire check flies due west from an airstrip and then turns around and flies due east back to the airstrip. The aircraft cruises at 100 m.p.h. when flying west and 125 m.p.h. when flying east. What is the farthest point from the airstrip the helicopter can reach if it remains airborne for 4 ½ hours?

10. Tracking a hurricane, an airplane flew due south from Miami at an average speed of 320 knots. Having located the eye of the storm the plane flew due north back to Miami at an average speed of 280 knots. If it was in the air for 3 hours, how far south did it fly?

11. On a cross country ski trip in a wilderness area, Ella and Jack skied at an average speed of 3 m.p.h. to a frozen lake where they stopped for lunch. Because the return trip was slightly more uphill, they made the return trip at an average speed of 2 m.p.h. If the actual travel time for the trip was 6 hours, how far from the camp was the frozen lake?

12. An express train made the trip from Edgerton to Carlisle in 4 hours. It traveled 20 m.p.h. faster than a freight train that took 6 hours for the same trip. Find the average speed of each train?

13. Traveling toward each other, a hovercraft and a car ferry are 86 nautical miles apart. If the average speed of the hovercraft is 20 knots greater than that of the ferry, and they meet in 2 hours, find the average speed of both craft .

14. An eastbound bus left Redfield at 8:00 a.m. and headed for Stanton, which is 240 miles away. At 9:00 a.m., a westbound bus left Stanton and traveled toward Redfield at an average rate that was 15 m.p.h. faster than the average rate of the other bus. Find the speed of the fast bus if it pass the slower on at 11:00 a.m. on the same day.

15. A refrigerator shi must average 20 knots to make it 12 hour run on schedule. During the first 3 hours, bad weather forced the captain to reduce speed to 14 knots. What should the speed of the ship be for the rest of the trip to keep on schedule?

16. An airplane had been flying for 2 hours when a change in wind decreased the plane’s ground speed by 45 m.p.h. If the entire trip of 960 miles took 3 hours, how far did the plane travel during the first two hours?

17. Miss Orloff drove from Hillside to Manor Haven at an average speed of 40 m.p.h. By traveling at an average rate of 48 m.p.h., she could have arrived 30 minutes earlier. How far is it from Hillside to Manor Haven?

18. In still water Bob can row 5 m.p.h. However, on the Red River it too him 3 hours to row upstream to his friends’ cabin and only 2 hours to return. Find the rate at which the river was flowing.

19. It ordinarily takes a bus 30 minutes to travel the 18 miles from the bus station at Clarksville to the airport. However during the rush hours of 4:00 p.m. to 6 :00 p.m., the bus can travel only 15 miles in the same length of time. If buses leave the station every hour and every half hour thereafter, and if it takes a person 15 minutes from the time he leaves a bus to get on an airplane, what is the last bus Janet Brandt can take from the station to make a plane leaving at 5:55 p.m.?

20 A turbojet train traveling 40 m.p.h. took 4 seconds to pass a man walking in the same direction at 4 miles per hour. How long was the train?

21. Two bees leave two locations 180 yards apart and fly, without stopping, continually back and forth between these two places at rates of 4 and 5 yards per second, respectively. When do the meet for a. the first time? b the second time?

22. A train running at the rate of 60 m.p.h. overtakes another train, 160 yards long, running 45 m.p.h. in the same direction on a parallel track and passes it in half a minute. How long would it take the first train to pass another of its own length going in the opposite direction at 30 miles per hour?