Two train stations are 50 miles apart. At noon, a train starts out from each station heading for each other. Just as they pull out, a hawk flies into the air in front of the first train and flies ahead to the front of the second train. When the hawk reaches the second train, it turns around and flies toward the first train. The hawk continues this way until the trains meet. Assume that both trains travel at 25 mph and the hawk flies at a constant speed of 100 mph. How many miles will the hawk have flown when the trains meet?

Question

Cassius

Mathematics

15 February, 11:13

Two train stations are 50 miles apart. At noon, a train starts out from each station heading for each other. Just as they pull out, a hawk flies into the air in front of the first train and flies ahead to the front of the second train. When the hawk reaches the second train, it turns around and flies toward the first train. The hawk continues this way until the trains meet. Assume that both trains travel at 25 mph and the hawk flies at a constant speed of 100 mph. How many miles will the hawk have flown when the trains meet?

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Rashad Donaldson · Answer 1

Answer: 100 miles

Step-by-step explanation: How much time does the bird spend in flight? If you represent the problem in terms of the amount of time the bird is flying, then a solution is fairly straightforward. The two trains are 50 miles apart, and are approaching each other at a relative speed of 50 mph (25 + 25), so it will take one hour for them to meet. If the bird spends one hour flying at 100 mph, then it will traverse 100 miles before the trains meet.