An elephant leaves his home at 7am. and walks along a well travelled path until he reaches a friend's home 10 hours later (where an all night elephant party ensues) The next day the elephant leaves his friend's house at 7am. and returns home in the same amount of time taking the same path. If f(t) represents the distance from his home on the first day and g(t) represents the distance from his home on the second day and t represents the time in hours modulo 24 (1e. a particular t value represents the same time on any given day), prove that there is at least one time where the elephant was at the exact same spot on both days. That is' prove that there is a t* such that t') = 9(t'). You may assume that the elephant cannot teleport. (Hint: IVT)