October 22nd, 2013, 09:30 PM  #1 
Newbie Joined: Oct 2012 Posts: 13 Thanks: 0  Intermediate value theorem
A manatee leaves his home at 7a.m. and swims along a well travelled path until he reaches a friend's home 10 hours later (where an all night manatee party ensues). The next day the manatee leaves his friend's house at 7a.m. and returns home in the same amount of time taking the same path. If f(t) represents the distance from his home on the rst day and g(t) represents the distance from his home on the second day and t represents the time in hours modulo 24 (i.e. a particular t value represents the same time on any given day), prove that there is at least one time where the manatee was at the exact same spot on both days. That is, prove that there is a t such that f(t) = g(t). You may assume that manatees cannot teleport. My professor told us to use intermediate value theorem to solve this. I tried doing f(t) g(t) = 0, but I need to find a value for t such that f(t)g(t) <0 and a value where f(t)g(t) > 0, what could I sub in to the function to make this true? 
October 23rd, 2013, 01:32 AM  #2 
Senior Member Joined: Feb 2013 Posts: 281 Thanks: 0  Re: Intermediate value theorem
what about the points 7a.m. and 5p.m?


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