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Distance Word Problem

This problem involves two trains that start 150 miles apart and travel towards each other, with speeds of 60 mph and 90 mph, respectively. A fly, traveling at 120 mph, continuously flies back and forth between the two trains until they collide. By determining the time it takes for the trains to meet, we can calculate the distance the fly travels during this time. This example illustrates the use of algebraic equations to solve real-world problems, involving patterns, relationships, and algebraic thinking.

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Distance Word Problem

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  1. Distance Word Problem Nicole Toy CUIN 3111

  2. TEKS (8.5)  Patterns, relationships, and algebraic thinking. The student uses graphs, tables, and algebraic representations to make predictions and solve problems. The student is expected to: (A)  predict, find, and justify solutions to application problems using appropriate tables, graphs, and algebraic equations; and (B)  find and evaluate an algebraic expression to determine any term in an arithmetic sequence (with a constant rate of change).

  3. The Problem Two trains 150 miles apart are traveling toward each other along the same track. The first train goes 60 miles per hour; the second train rushes along at 90 miles per hour. A fly is hovering just above the nose of the first train. It buzzes from the first train to the second train, turns around immediately, flies back to the first train, and turns around again. It goes on flying back and forth between the two trains until they collide. If the fly's speed is 120 miles per hour, how far will it travel?

  4. The Equation D=RT Distance Rate Time 60 miles/hour 90 miles/hour

  5. What’s Given Train 1: Traveling 60 miles/hour Train 2: Traveling 90 miles/hour Fly: Traveling 120 miles/hour

  6. Solving… -The first train is traveling at 60 miles/ hour -The second train is going 90 miles/ hour -They are approaching each other at: 60 miles/ hour + 90 miles/ hour = 150 miles/ hour. Distance = Rate * TimeTime = Distance / Rate= (150 miles) / (150 miles/ hour)= 1 hour.

  7. The Answer As we discovered earlier, the trains will travel 1 hour before they collide. Since the fly is traveling 120 miles/hour it will travel 120 miles. Distance = Rate * Time D = 120 miles/hour * 1 hour D = 120 miles 1 hour later

  8. Resources • Website • www.mathforum.org

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