Bit of high school algebra will do it.
If we assume that t=time in minutes, s=distance in nautical miles.
At t=0 (actually 10am), Aircraft A is at distance 0, and aircraft B is at distance 300 (the other airfield).
So, position of A is (100/60)*t
And position of B is 300 - (150/60)*t
When they pass, the position is the same (obviously), so
(100/60)*t=300-(150/60)*t
Re-arrange that, and you get:-
( (100/60) + (150/60) ) * t = 300
Divide through by ( (100/60) + (150/60) ) and you get
t = 300 / ( (100/60) + (150/60) )
Which comes out at 72 minutes by my calculator.
So, they'll pass each other at 11:12.
And if you want the position, just use aircraft A: (100/60)*72 = 120nm. So they meet 120Nm from airport A.
To double check, put aircraft B's equation in: 300 - (150/60)*72 = 120, same answer.
G