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Motion Problems 2

This document presents a series of motion problems involving two individuals using different modes of transportation. Each problem requires determining the distance traveled based on given speeds and time differences. The Rate-Time-Distance (R.D.T.) method is applied to establish equations correlating distance, speed, and time for various scenarios. From biking to driving, these examples illustrate how to strategically set up equations to find unknowns, helping students grasp the dynamics of travel and motion concepts.

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Motion Problems 2

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  1. Motion Problems 2

  2. A man bikes from A to B at 20 km/h. He returns by car at 60 km/h. The bike trip is 2 hours longer than the car trip. How far is it from A to B?

  3. Which one?

  4. R D T = Method X The distance is always filled in by multiplying the rate and time. 20 Bike 20(x + 2) x + 2 Car 60 x 60x Distances are equal.

  5. 20(x+2) = 60x 20x+40 = 60x -20x -20x 40 = 40x 40 40 1 = x

  6. A man bikes from A to B at 20 km/h. He returns by car at 60 km/h. The bike trip is 2 hours longer than the car trip. How far is it from A to B?

  7. R D T = Method X 20 Bike 20(x + 2) x + 2 Car 60 x 60x What does x represent? What represents distance?

  8. If x=1, distance is: 60x=?? 60x=60 20(x+2)=?? 20(x+2)=60

  9. The answer is: 60 km

  10. Problem #2 on Worksheet 61

  11. Vince bikes for 2 hours at 18 km/h. Then he rides by car for 3 hours. His total distance is 246 km. How fast does the car travel?

  12. Which one?

  13. None of those. It’s this one: The distances add up to the total distance.

  14. R D T = Method X The distance is always filled in by multiplying the rate and time. 36 2 18 Bike 3 3x x Car 246

  15. 36+3x = 246 -36 -36 3x = 210 3 3 x=70

  16. R D T = Method X 36 2 18 Bike 3 3x x Car 246 What does x represent?

  17. Vince bikes for 2 hours at 18 km/h. Then he rides by car for 3 hours. His total distance is 246 km. How fast does the car travel?

  18. The answer is: 70 km/h

  19. Problem #3 on Worksheet 61

  20. Cindy bikes from A to B at 20 km/h. She returns by car at 80 km/h. The bike trip is 3 hours longer than the car trip. How far is it from A to B?

  21. Which one?

  22. R D T = Method X The distance is always filled in by multiplying the rate and time. x+3 20 Bike 20(x+3) x 80x Car 80 Distances are equal.

  23. 20(x+3) = 80x 20x+60 = 80x -20x -20x 60 = 60x 60 60 1=x

  24. R D T = Method X x+3 20 Bike 20(x+3) x 80x Car 80 What does x represent?

  25. Cindy bikes from A to B at 20 km/h. She returns by car at 80 km/h. The bike trip is 3 hours longer than the car trip. How far is it from A to B?

  26. The answer is: 80x= 80(1)= 80 km

  27. Problem #4 on Worksheet 61

  28. Judy can bike 2 km/h faster than Linda. They travel in opposite directions for 2 hours. They are then 68 km apart. How fast is each girl traveling?

  29. Which one?

  30. R D T = Person X The distance is always filled in by multiplying the rate and time. 2 Judy x+2 2(x+2) 2 2x Linda x 68

  31. 2(x+2)+2x = 68 2x+4+2x = 68 4x+4 = 68 -4 -4 4x= 64 4 4 x=16

  32. R D T = Person X 2 Judy x+2 2(x+2) 2 2x Linda x 68 What does x represent?

  33. x=Linda’s rate of speed x= 16 km/h x+2=Judy’s rate of speed x+2= 18 km/h

  34. THE END

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