The energetic dog

Algebra Level 5

A boy and his dog are climbing a mountain. When the boy is 100m from the summit, his dog starts to run to the summit of the mountain. When it reaches the summit, it runs down the slope again. When the dog reaches the boy this time, he starts to run to the summit the second time, and this process continues until both have reached the top of the mountain. What is the length of the journey his dog has run? Details:

  • The speed of the dog when running uphill is 3m/s.
  • The speed of the dog when running downhill is 5m/s.
  • The speed of the boy is 1m/s.

Note: If your answer is, for example, 400m, write 400 in the answer space.

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