Problem of the Week #6:  (Fall, 2014, for the week of 9/22/2014 – 9/26/2014)

We have very eccentric neighbors who both insist on walking their dog at the same time.  They use two separate leashes on the poor animal.  Each leash is 1 m long, and the distance between the neighbors as they walk is also consistently 1 m.  If they are stopped on the sidewalk, what is the area of the region in which the dog is free to roam?  Clearly show the mathematical process that you use to find your solution.

Solutions are due at or before noon, Friday September 26.



  1. This contest is open to any students who are registered at Sinclair for the Fall semester of 2014.  It is expected that students will work alone on the problems.
  2. Weekly problems will be posted on the board in the Math Help Room Monday mornings.  Solutions to a problem will appear there the following week.
  3. All answers must be substantiated by hand for credit (show all work).  Programs written to solve the problem by computer or calculator will not count as sufficient justification.
  4. Submit solutions to Susan Harris in room 01-331.  You may slip them under her office door anytime before Friday at noon.
  5. Names of all students who submit correct solutions on time will be posted by the following week.
  6. A prize of $50 will be awarded to the student who correctly answers the most problems for the quarter, and a prize of $25 will be awarded to the second place winner.


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