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The Trains and the Bird (illustration)
FILE No.199Unsolved

The Trains and the Bird

Difficulty ★★☆about 5 minLogic PuzzleSpeedTime
Two trains 100 km apart head toward each other at 50 km/h. A bird flies back and forth at 80 km/h. How far does the bird fly?

Case Record

From 100 km apart, two trains start running toward each other, each at 50 km/h. A bird takes off from the front of one train at 80 km/h and heads for the other train. On arrival it immediately turns around, and keeps flying back and forth until the two trains meet.

Your question

What is the total distance the bird flew, in kilometers?

Case Files

Diagram

Two trains approaching50 km/h50 km/h100 km apart. A bird flies back and forth at 80 km/hHow far does the bird fly before the trains meet?
Diagram

Hints

If you get stuck, open the hints one at a time, in order.

Open hint 1

How many hours until the two trains meet?

Open hint 2

The bird is flying the whole time.

Open hint 3

Distance is speed times time.

Solve It

Your question

What is the total distance the bird flew, in kilometers?

Choose the answer closest to the truth.

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The Truth

80 km

The answer is "80 km."

The trains approach each other at 50 km/h each, so it takes 1 hour to close the 100 km. The bird flies at 80 km/h the whole time, so it flies 80 km.

You do not need to count the number of round trips; you can get it from "time × speed."

Use time, not the number of tripsItemDetailClosing speed50 + 50 = 100 km/hTime to meet100 km ÷ 100 km/h = 1 hBird1 h × 80 km/h = 80 km
Diagram of the solution

Key Points

  • Find the total time first
  • Do not count the round trips
  • Calculate with speed × time

Why people get fooled

Because you try to add up the distance of each trip one by one.

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