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VARIABLES ON BOTH SIDES STORY PROBLEMS

This article explores two practical problems involving cost calculations for car rentals and distance-time relationships in travel. The first scenario compares rental costs between two companies, Rent-a-Wreck and Lemon Leasers, helping determine the mileage at which the costs are equal. The second scenario examines how long it takes Jane to catch up to her brother Joe after he leaves for a walk. Using the principles of algebra, we analyze the equations and find the solutions step-by-step, providing a clear understanding of solving real-world math problems.

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VARIABLES ON BOTH SIDES STORY PROBLEMS

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  1. VARIABLES ON BOTH SIDES STORY PROBLEMS “THE TOUGH STUFF”

  2. A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same?

  3. A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same? • Cost for Rent-a-wreck = 60 + .2m

  4. A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same? • Cost for Rent-a-wreck = 60 + .2m • Cost for Lemon Leasers = 30 + .5m

  5. A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same? • Cost for Rent-a-wreck = 60 + .2m • Cost for Lemon Leasers = 30 + .5m • Set the two equal to each other

  6. A business representative is looking to rent a car. Rent-a-wreck charges $60 per day plus $0.20 per mile. Lemon Leasers charges $30 per day plus $0.50 per mile. At what miles are the costs the same? • Cost for Rent-a-wreck = 60 + .2m • Cost for Lemon Leasers = 30 + .5m • Set the two equal to each other • 60 + .2m = 30 + .5m

  7. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  8. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? • This is a “same direction” problem.

  9. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? • This is a “same direction” problem. • When going the same direction, the distances are equal.

  10. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? • This is a “same direction” problem. • When going the same direction, the distances are equal. • Use the formula d = rt

  11. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  12. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  13. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  14. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  15. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  16. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  17. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  18. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  19. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe?

  20. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? Set the distances equal to each other and solve.

  21. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? Set the distances equal to each other and solve.

  22. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? Set the distances equal to each other and solve.

  23. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? Set the distances equal to each other and solve.

  24. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? Set the distances equal to each other and solve.

  25. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? The t solved for was the time that JOE was on the road. Jane’s time was (t – 15), or 45 minutes.

  26. Joe leaves his house and travels at a rate of 6 mi/h. His sister, Jane, realizes that Joe has forgotten his lunch and goes after him 15 minutes later. She travels at a rate of 8 mi/h. How long does it take Jane to catch up to Joe? **BE SURE TO ANSWER THE QUESTION ASKED.

  27. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  28. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  29. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  30. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  31. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  32. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  33. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  34. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  35. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  36. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  37. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  38. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  39. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  40. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  41. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  42. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  43. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will?

  44. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will? Is 7 hours the answer to the question??

  45. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will? Is 7 hours the answer to the question?? This question asked for “what time”. That means the actual clock time.

  46. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will? Since t was the time for Will, add 7 hours to his departure time.

  47. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will? Since t was the time for Will, add 7 hours to his departure time. Will left at 6:00 am. Wayne catches him 7 hours later, or at 1:00 pm

  48. Will takes a bus to Cedar Point. He leaves at 6:00 am and travels at a rate of 50 mi/h. Wayne rides in a car with his friends and follows the same route. If Wayne leaves at 8:00 am, and travels at a rate of 70 mi/h, at what time does Wayne catch up to Will? Since t was the time for Will, add 7 hours to his departure time. Will left at 6:00 am. Wayne catches him 7 hours later, or at 1:00 pm **Be sure to include the proper am vs. pm designation

  49. ASSIGNMENT • 7-5: 17, 28, 33, 35 - 40

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