Question 818401
It is a rate of work problem that you need to break down into several parts. My favorite!
normally
x/3+x/4=1
4x/12+3x/12=1
7x/12=1
x=12/7 working together
This is what we expect with BUT IT IS NOT the question.
We have three times we need to use
t for time together 
a for time arguing 
p for pat's time alone
t+a+p=2+25/60,
a=10/60,
t/3+t/4+ p/4=1
we have three unknowns and three equations
It can be solved
a = 1/6,   p = 15/16,   t = 21/16 in hours
a=0.16667,   p=0.93750,   t=1.3125 in hours
a = 10,   p = 225/4,   t = 315/4 in minutes
a=10,   p=56.250,   t=78.750 in minutes
They worked 21/16 hours or 78.75 minutes together
they argued at 1:18:45 pm
They argued for 10 minutes

Pat worked 15/16 of an hour alone



we could have converted everything to minutes to begin with
t+a+p=145,
 a=10,
 t/180+t/240+ p/240=1
t+a+p=145, a=10, t/180+t/240+ p/240=1
we get the same answers
a = 10,   p = 225/4,   t = 315/4 in minutes
a=10,   p=56.250,   t=78.750 in minutes