rate * time = distance.
Let x = number of hours Kathy drove.
Let y = number of hours Brian drove.
The total distance traveled is the distance Kathy drove plus the distance Brian drove. But we don't know how far they drove, and we don't have a variable for it. But we do have a variable for how many hours each one drove, and we have the formula rate * time = distance.
750 = distance Kathy drove + distance Brian drove.
750 = 65 x + 55 y
We know that between the two of them, they drove for 12 hours.
12 = x + y
You have two equations and two unknowns. multiply the second equation by -55 to get
-660 = -55 x - 55 y
Then add the first equation to this one to get:
90 = 10 x
So Kathy drove for 9 hours and Brian drove for the remaining 3 hours.

K.J. P.
04/02/19
Maggie H.
That is what I got close to, although I think it's the other way around: Kathy 3 hours Brian 9 hours. Thank you!04/02/19