At t, OP is 1 10+5t, and OQ is 40 +5t.
Om divides the ∠POQ equally,
So OM is (110+5t+40+5t)/2 = 75+5t,
In equal shares ∠POA,
The analogy is (110+5t)/2 = 55+2.5t,
So ∠ mon = 75+5t-(55+2.5t) = 20+2.5t = 40,
The solution is t=8 (minutes).
Is it okay?