Difference between revisions of "2013 AMC 12B Problems/Problem 11"
(Tag: Undo) |
m |
||
Line 11: | Line 11: | ||
Thus they reach 10 feet away when A is moving east and B is moving west, between moves 7 and 8. Thus the answer is <math>\textbf{(A)}</math> | Thus they reach 10 feet away when A is moving east and B is moving west, between moves 7 and 8. Thus the answer is <math>\textbf{(A)}</math> | ||
− | |||
− | |||
− | |||
− | |||
== See also == | == See also == | ||
{{AMC12 box|year=2013|ab=B|num-b=10|num-a=12}} | {{AMC12 box|year=2013|ab=B|num-b=10|num-a=12}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Latest revision as of 15:47, 27 November 2019
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?
east, west
north, south
north, west
up, south
up, west
Solution
Let A and B begin at (0,0,0). In 6 steps, A will have done his route twice, ending up at (2,2,2), and B will have done his route three times, ending at (-3,-3,0). Their distance is We now move forward one step at a time until they are ten feet away: 7 steps: A moves north to (2,3,2), B moves south to (-3,-4,0), distance of 8 steps: A moves east to (3,3,2), B moves west to (-4,-4,0), distance of
Thus they reach 10 feet away when A 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 |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.