Here is my answer to the challenge. I kept it as simple as I could and I think this is right. To be honest I'm not entirely sure I have my calculations correct in terms of travel and full days for projects that press up against each other or overlap, but I do believe my answer is solid and can be used with any data long as said data is in the same format.
to run clone down, cd into the folder and run ruby reimburse_me.rb