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DISTANCE: (d=rt)

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# 1. You drive down the road at 55 miles per hour for two hours. How far do you go? __________

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# 2. You drive down the highway at 65 miles per hour for twenty minutes. How far do you go? ____________

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**We drive for 4 hours and go 190 miles. What was our average speed?**

# 3. We drive for 4 hours and go 190 miles. What was our average speed? ____________

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**________________________**

Two trains start at the same point. One train travels east at 40 miles per hour for at least 4 hours. The other train travels west at an unknown speed. Four hours later the trains are 360 miles apart. What was the average speed of the second train? ________________________ # 4.

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# 5. A bus traveling at an average rate of 50 kilometers per hour made the trip to town in 6 hours. If it had traveled at 45 kilometers per hour, how many more minutes would it have taken to make the trip? __________________

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# 6. A bus and a car leave the same place and traveled in opposite directions. If the bus is traveling at 50 mph and the car is traveling at 55 mph, in how many hours will they be 210 miles apart? ____________

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# 7. John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John? _______________

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# 8. Into the headwind, the plane flew 200 miles in 5 hours. With a tailwind, the return trip took 4 hours. Find the speed of the plane in still air and the speed of the wind. _________________

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# 9. Two planes A and B can each fly through still air at 450 mph. The distance from Paris to Los Angeles is 5000 miles. Wind blows from Los Angeles towards Paris at a speed of 100 mph. Plane A leaves Paris at noon flying towards Los Angeles. Plane B departs Los Angeles 1 hour later to fly to Paris. How far from Los Angeles are the two planes when they pass each other? __________________________ miles

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# 10. A cyclist starts at a certain point and rides at a rate of 10 mph. Twelve minutes later, another cyclist starts from the same point in the same direction and rides at 16 mph. How long will it take for the second cyclist to catch up with the first? __________

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# 11. A car passes an intersection heading north at 40 mph. Another car passes the same intersection 15 minutes later heading north traveling at 45 mph. How long will it take for the second car to overtake the first? _______

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# 12. Two cars meet at an intersection, one heading north; the other, south. If the northbound driver drives at 30 mph and the southbound driver at 40 mph, when will they be 35 miles apart? __________

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# 13. Two friends leave a hotel at the same time traveling in opposite directions. They travel for four hours and are then 480 miles apart. If Susan travels 10 miles per hour faster than Joan, find the average rate of speed for each person. Susan: ___________ Joan: _____________

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# 14. A runner decides to run out in the country. He begins to run at an average rate of 9 miles per hour. He runs a certain distance and then turns around and returns along the same route at an average rate of 6 miles per hour. If the round trip took 2 ½ hours, how far did the runner travel before turning around? ________

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# 15. A 555-mile, 5-hour plane trip was flown at two speeds. For the first part of the trip, the average speed was 105 mph. Then the tailwind picked up, and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed?

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# 16. An executive drove from home at an average speed of 30 mph to an airport where a helicopter was waiting. The executive boarded the helicopter and flew to the corporate offices at an average speed of 60 mph. The entire distance was 150 miles. The entire trip took three hours. Find the distance from the airport to the corporate offices. _______________

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# 17. A car and a bus set out at 2 pm from the same point, headed in the same direction. The average speed of the car is 30 mph slower then twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car. ______________

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# 18. A passenger train leaves the train depot 2 hours after a freight train left the same depot. The freight train is traveling 20 mph slower then the passenger train. Find the rate of each train, if the passenger train overtakes the freight train in three hours. _____________

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# 19. A train leaves Deb’s house and travels at 50 miles per hour. Two hours later, another train leaves from Deb’s house on the track beside or parallel to the first train but it travels at 100 miles per hour. How far away from Deb’s house will the faster train pass the other train? ______________

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# 20. One train left the station and traveled toward its destination at a speed of 65 miles per hour. Later, another train left the station traveling in the opposite direction of the first train, was going at a speed of 75 miles per hour. After the first train had traveled for 14 hours, it was miles apart from the second train. How long did the second train travel? ______________

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# 21. Suppose two sisters live 240 miles apart. One sister has three young children who are planning to visit their aunt for a week. To prevent driving so far, the sisters agree to leave at the same time, drive toward each other, and meet somewhere along the route. The sister with the three children tends to drive carefully and obey the speed limit. Her average rate of speed is 70 mph. The other sister drives too fast, and her average rate of speed is 80 mph. How long will it take the sisters to meet each other to transfer the children? ___________

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Introduction to Distance-Rate-Time Applications Example 1: Jan drives south out of Denver and averages 65mph. How far is she from Denver after 3 hours.

Introduction to Distance-Rate-Time Applications Example 1: Jan drives south out of Denver and averages 65mph. How far is she from Denver after 3 hours.

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