Mileage Log To Record Specific Distances?

I'm creating a mileage log for my work as a traveling art teacher. Most templates have you just input the number on the odometer when you started and when you finished. Since I can never remember to check the odometer when I am getting in and out of the car I thought it might be easier to just record the distance from each location once and then record that number of miles each trip. I usually travel the same route so the mileage is always the same.

I have an array of numbers right now, with 3 columns listing my 3 most common start locations. Then I have 5 rows listing the 5 schools I travel to for work, and the distances from each start to each end in the array. On a separate sheet I have my log.

What I would like to be able to do is select a start location and an end location from a drop down list on the log and have the number of miles automatically appear in the miles column. Then I can double this for the return trip and total it at the bottom and calculate my expense.

I am having trouble writing a formula that works for all 15 possible distances, and I don't quite know how to write it so that it references my array and finds the correct distance for those two specific choices. So far I have the drop down menu's pulling from the array but I'm stuck at how to index the array using the information that is coming from the drop down list.

Since I travel to these locations multiple times I think it would be a lot faster than looking up the distance every time and typing it up manually.