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 have no idea how to set up the two equations f(t) and g(t) into one

so I can apply the IVT.