I am able to solve this sort of problem pretty easily.
An arm wrestler is the champion for a period of 75 hours. The arm wrestler had at least one match an hour, but no more than 125 total matches. Show that there is a period of consecutive hours during which the arm wrestler had exactly 24 matches.
However this homework problem I can't seem to figure out.
Tyler has five weeks to prepare for his driver’s test. His mother volunteers to ride with him for either 15 minutes or one half hour every day until the test but not for more than 15 hours in all. Show that during some period of consecutive days, Tyler and his mother will drive for exactly 8.75 hours.
If I try doing it the same way as the first problem. I get $70$ pigeons and $95$ pigeon holes. I honestly don't know where to start with this problem. I thought that maybe I could assume that they only drove $.25$ hours on each day and prove that there is a period of consecutive days where they drove for exactly $8.75$ hours. Then I could say that we assume there is one day that they drove for $.5$ hours and work my way up, but I can't seem to get that to work either.