2013 AMC 12B Problems/Problem 11
Problem
Two bees start at the same spot and fly at the same rate in the following directions. Bee travels foot north, then foot east, then foot upwards, and then continues to repeat this pattern. Bee travels foot south, then foot west, and then continues to repeat this pattern. In what directions are the bees traveling when they are exactly feet away from each other?
Solution
Let A and B begin at . In steps, will have done his route twice, ending up at , and will have done his route three times, ending at . Their distance is We now move forward one step at a time until they are ten feet away:
7 steps: moves north to , moves south to , distance of
8 steps: moves east to , moves west to , distance of
Thus they reach feet away when is moving east and B is moving west, between moves 7 and 8. Thus the answer is .
See Also
2013 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 10 |
Followed by Problem 12 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
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