The Race of the Ants

     Two ants, whose names are Ant M and Ant B, often compete with each other to see who can be the first to grab a sweet morsel of food. Ant B, the faster runner of the two, always runs at twice the speed of Ant M.

     One day they both saw a particularly inviting crumb of bread that was 100 cm directly to the east of Ant M. At that moment Ant B happened to be some distance straight north of Ant M's position.

     At the signal "1, 2, 3, GO!", they both ran to the crumb of bread, arriving at the same moment. A tie! So they decided to share it.

     Your task for this problem is to determine just how far north of Ant M was Ant B at the start of this little race.

Variations:

  1. If Ant B's starting position had been directly to the west of Ant M, how far apart would the two characters have been initially?

  2. If Ant B's starting position had been directly to the northwest of Ant M, how far apart would the two characters have been initially?

  3. If Ant B's starting position had been directly to the east of Ant M, how far apart would the two characters have been initially?

  4. If Ant B's starting position had been directly to the northeast of Ant M, how far apart would the two characters have been initially?

  5. If Ant B's starting position had been directly to the north of the crumb of bread, how far apart would the two characters have been initially?

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