Pedals on a Bicycle

Balance an ordinary bicycle upright without restraining its motion in any way. Position the pedals so that they are top-and-bottom. Standing on the ground alongside the bike without mounting it, grasp the top pedal and push it forwards (in the normal direction of travel). The pedal moves forward and so does the bike of course. Now, reposition the pedals as before, but this time grasp the lower pedal and push backwards. Three questions:
  1. Which way does the bike move?
  2. Which way does the pedal move?
  3. Why?
(Try to solve this puzzle in your head before referring to an actual bicycle.)

Source: Reader Peter Bentley, citing someone named "Jellio".

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