I appreciate the problem at hand.
Since we need to calculate the 'half', we can consider that
Daily quota of Machine Red is 100
=>Daily quota of Machine Blue is 1.2(100)=120
Each operates for 10 hours a day, then
Rate = Daily quota/Daily operating hours
Blue works till 10:45 alone and does 33 units of work.
We have to complete half of (100+120) => 110
Remaining units = 77
Rate(Blue) + Rate (Red) = 22
Remaining Work/Rate = TIme
10:45 + 3.5 hours = 14:15
Hope that helps !
I Assisted You => KUDOS Please