Agents J and K work in a long hallway with 4000 equally-spaced, consecutive offices. The agents decide to walk toward each other so they can meet and have lunch together. Agent J has recently been relocated from office 2013 to office 1. His former office neighbor, agent K, is still in office 2014. Assuming that Agent J can walk at a rate of 25 offices per minute, and Agent K walks at 36 offices per minute, what office will they meet at if they leave at the same time?
To find the office where Agents J and K will meet, we need to determine the time it takes for each agent to reach the meeting point.
Agent J starts at office 1 and walks at a rate of 25 offices per minute. Therefore, it will take Agent J a total of (2014 - 1) / 25 = 80.52 minutes to reach office 2014.
Agent K starts at office 2014 and walks at a rate of 36 offices per minute. It will take Agent K a total of (2014 - 2014) / 36 = 0 minutes to reach office 2014, as he is already there.
So, both agents will meet after 80.52 minutes, since Agent K is already at office 2014. To find the meeting office, we need to determine how many offices Agent J will walk in that time.
Since Agent J walks at a rate of 25 offices per minute, after 80.52 minutes, Agent J will walk a total of 80.52 x 25 = 2013 offices.
Therefore, the meeting office will be office 2014 (K's office) plus the number of offices Agent J walks in that time, which is 2014 + 2013 = 4027.
Thus, Agents J and K will meet at office 4027.