Conditional SumProduct To Evaluate Iteratively

I have two tables, one summary sheet which contains a list of 30 projects. The second sheet has the projects broken down by task and status ("on time" or "late"), so it has three columns (project, task and status). I am trying to add up the number of projects within each task that are either "on time" or "late" and put these in two columns, so that the sum of each together will always equal 30.

The trouble is that any given task can appear multiple times for a project, and if one instance of that task is late, I want to count the whole project late for that task. Here is a table of what I am trying to do:

Project Task Status
A1 MU On time
A1 MU Late
A1 FA On time
B2 FA On time
B2 MU On time
B2 MU On time

The desired result of this scenario is that under task "MU" I would show a count of 1 projects on time (B2), and one that is late (A1). For task "FA" I would show a count of 2 projects "on time" (A1 and B2) and none for "late"

I think that an array formula is needed where it assigns a 1 to a project and task that is on time, and a 0 if it is not, and then multiplies these figures for each project and adds them up.