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Two Amtrak commuter trains travel across a mid-western state. Each has a speed of 20 km/h, are headed at each other on the same straight track. A hawk that can fly 60 km/h flies off the front of one train when they are 64 km apart and heads directly for the other train. On reaching the other train it flies directly back to the first train, and so forth. What is the total distance the hawk travels?

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onyebuchinnaji

The total distance traveled by the hawk during motion is 96 km.

The given parameters;

  • speed of each train, V₁ and V₂ = 20 km/h
  • speed of the hawk, = 60 km/h
  • distance between the train, = 64 km

To determine the total distance traveled by the hawk, we will assume that the hawk flies continuously until the two trains meet each other.

The time for the two trains to meet each other is calculated as follows;

[tex](V_1 - (-V_2)) t = distance \ apart\\\\(V_1 + V_2 )t = distance \ apart\ \\\\(20 + 20) t = 64\\\\t = \frac{64}{40} \\\\t = 1.6 \ hours[/tex]

The total distance traveled by the hawk is calculated as follows;

total distance = speed x time of motion

[tex]total \ distance = 60 \ \frac{km}{h} \times 1.6 \ h\\\\total \ distance = 96 \ km[/tex]

Thus, the total distance traveled by the hawk during motion is 96 km.

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