Write your code like:
File.open("exercise.txt", "r") do |fi|
file_content = fi.read
puts "This is an exercise log. It keeps track of the number hours of exercise."
hours = gets.chomp.to_f
end
Ruby's File.open takes a block. When that block exits File will automatically close the file. Don't use the non-block form unless you are absolutely positive you know why you should do it another way.
chomp the value you get from gets. This is because gets won't return until it sees a trailing END-OF-LINE, which is usually a "\n" on Mac OS and *nix, or "\r\n" on Windows. Failing to remove that with chomp is the cause of much weeping and gnashing of teeth in unaware developers.
The rest of the program is left for you to figure out.
The code will fail if "exercise.txt" doesn't already exist. You need to figure out how to deal with that.
Using read is bad form unless you are absolutely positive the file will always fit in memory because the entire file will be read at once. Once it is in memory, it will be one big string of data so you'll have to figure out how to break it into an array so you can iterate it. There are better ways to handle reading than read so I'd study the IO class, plus read what you can find on Stack Overflow. Hint: Don't slurp your files.