Distance = Time x Rate, or Rate = Distance / Time. We're given Time, and the Distance in terms of p and q.

Since we know total time was 5 hours, Mary traveled for 3 hours at the rate of q. So, we can interpret the first part as:
$2p+3q =D$, where D is total distance traveled.

We're also given $p+\frac{3}{2}q=140$
Multiply both sides by 2:
$2(p+\frac{3}{2}q)=2*140$
$2p+3q=280=D$

However, we want to find the Rate:
$= D/5 = 280/5 = 56$