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Systems of Equations

Solve motion problems by identifying variables, writing systems, algebraically solving, and answering in words with reality check. Windy Problems included.

jcarmen
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Systems of Equations

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  1. Systems of Equations Application Problems: Motion - With / Against KM & PP

  2. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  3. Motion Problem Basics d = r t d = distance r = rate t = time KM & PP

  4. Motion Problem Basics d = r t The distance you travel is equal to the rate at which you are traveling multiplied by the time you travel. KM & PP

  5. Motion Problem Basics d = r t KM & PP

  6. Windy Problems ? + - Tail Wind Head Wind With the Wind Against the Wind Speeds you up Slows you down KM & PP

  7. Word Problem Basics • IDENTIFY VARIABLES • p = speed of the plane • w = speed of the wind • d = distance • r = rate • t = time KM & PP

  8. Generic Box With - Tail Wind Against - Head Wind KM & PP

  9. Come fly with me! Flying with the wind, a jet flew 7 hours with a 40 mph tail wind. The return flight, against the same wind took 8 hours. Find the speed of the plane in calm air. KM & PP

  10. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  11. Word Problem Basics • IDENTIFY VARIABLES • p = speed of the plane • d = distance KM & PP

  12. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  13. Come fly with me! With - Tail Wind Against - Head Wind KM & PP

  14. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  15. Come fly with me! Substitute for d KM & PP

  16. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  17. Come fly with me! Flying with the wind, a jet flew 7 hours with a 40 mph tail wind. The return flight, against the same wind took 8 hours. Find the speed of the plane in calm air. The speed of the plane in calm air is 600 mph. KM & PP

  18. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  19. Let’s go flying! Flying with the wind, a small plane flew 300 miles in 2 hours. Against the wind the plane could only fly 270 miles in the same amount of time. Find the rate of the plane in calm air and the rate of the wind. KM & PP

  20. Word Problem Basics • IDENTIFY VARIABLES • p = speed of the plane • w = speed of the wind KM & PP

  21. Write a COMPLETE SYSTEM. With - Tail Wind Against - Head Wind KM & PP

  22. Algebraically SOLVE the SYSTEM. KM & PP

  23. Let’s go flying! Add the Equations KM & PP

  24. Let’s go flying! Replace p in the top equation with 142.5. Solve for w. KM & PP

  25. CLEARLY ANSWER the question(s) in WORDS Flying with the wind, a small plane flew 300 miles in 2 hours. Against the wind the plane could only fly 270 miles in the same amount of time. Find the rate of the plane in calm air and the rate of the wind. The speed of the plane in calm air is 142.5 mph and the wind speed is 7.5 mph. KM & PP

  26. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  27. Boating Problems ? + - Downstream - Upstream - With the Current Against Current Speeds you up Slows you down KM & PP

  28. Word Problem Basics • IDENTIFY VARIABLES • d = distance • r = rate • t = time • b = speed of the boat • c = speed of the current KM & PP

  29. Generic Box With - Downstream Against - Upstream KM & PP

  30. Let’s Canoe! A canoeist paddled for 3 hours with a current of 4-km/hr. Against the 4-km/hr current, the canoeist returned home in 5 hours. Find the rate of the boat in calm water. KM & PP

  31. Word Problem Basics • IDENTIFY VARIABLES • b = speed of the boat • d = distance KM & PP

  32. Write a COMPLETE SYSTEM With - Downstream Against - Upstream KM & PP

  33. Algebraically SOLVE the SYSTEM. Substitute for d KM & PP

  34. CLEARLY ANSWER the question in WORDS. A canoeist paddled for 3 hours with a current of 4-km/hr. Against the 4-km/hr current, the canoeist returned home in 5 hours. Find the rate of the boat in calm water. The speed of the boat in still water is 16-km/hr KM & PP

  35. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  36. How about boating? A motorboat traveling with the current went 72-km in 3 hours. Against the current, the boat could go only 48-km in the same amount of time. Find the rate of the boat in calm water and the rate of the current. KM & PP

  37. Word Problem Basics • IDENTIFY VARIABLES • b = speed of the boat • c = speed of the current KM & PP

  38. Write a COMPLETE SYSTEM. With - Downstream Against - Upstream KM & PP

  39. Algebraically SOLVE the SYSTEM. KM & PP

  40. How about boating? Add the Equations KM & PP

  41. How about boating? Replace b in the top equation with 20. Solve for c. KM & PP

  42. Clearly answer the question in words. A motorboat traveling with the current went 72-km in 3 hours. Against the current, the boat could go only 48-km in the same amount of time. Find the rate of the boat in calm water and the rate of the current. The speed of the boat is 20-kph in calm water. The speed of the current is 4-kph KM & PP

  43. Word Problem Basics • IDENTIFY your VARIABLES • Write a COMPLETE SYSTEM • Algebraically SOLVE the SYSTEM • CLEARLY ANSWER the question(s) in WORDS • REALITY CHECK ? Does your answer make sense? KM & PP

  44. That’s All for Now! KM & PP

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