Power Pivot :: Return Time Based Upon Sum Of Personnel Arriving At Fire Scene

As part of analyzing our fire department's response times, we measure the time it takes to get a certain amount of people on a fire scene. I have two table that contains incident data. The incident table contains one row per incident. The apparatus table contains multiple rows per incident with each row contain the information for each unit. They are connected by the incident key with a one to many relationship. 

The column apparatus.num_personnel contains the count of personnel for each fire truck. The goal is to capture the response time of the unit that is carrying the 10th person to the scene. In the example below, E78 was the unit that the sum of apparatus.num_personnel was => 10. There response time of 0:06:18 is returned to the incident table. 

I realize I will need to create a logical test (calculated column on the incident table) that sums the number of personnel for each incident and then when that number => 10, then return the MIN Response Time of that row. From past projects, I understand I can create a temporary table (ADD COLUMNS) which will iterate over each incident row, comparing the units for that incident. I"m just not sure how to put it all together. 

Overview of data model. The incident and apparatus are my data tables and the rest are lookup tables. The parameter table is used for a percentile measure, but doesn't play a role with this project.