Model Method - Questions and Answers



Question posted by Leslie from the United States:

Grade/Level: PreAlgebra/Algebra

Question: Train A leaves the station at 1pm going 20 mph. Train B leaves the same station an hour later (2pm) going 50 mph. When does Train B catch up to Train A?

Answer:

Step 1: Draw a line to represent the distance travelled by Train A before Train B catches up with it. Label the starting time to the left, i.e., 1pm. Let the distance travelled be "D".

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Step 2: Draw a line to represent the distance travelled by Train B before it catches up with Train A. Label the starting time to the left, i.e., 2pm. Similarly, the distance travelled should also be "D" since Train B would have to travel the same distance in order to catch up with Train A.

To the right, draw a long line to represent the point where Train B catches up with Train A.

Next, label the speed of both trains respectively, (20mph and 50 mph).

Let the time taken by Train B to travel distance "D" be "T". Therefore, the time taken by Train A to travel distance "D" will be "T + 1".

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Step 3: Next, we establish the relationship among the distance, time and speed of the two trains using the formula "Time = Distance / Speed".



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