L----------------M---------------N

L point of overtake.
M point where B is when A reaches N ( town ).

LM = y miles ; MN = 35 miles
Speed of B = X mph
Speed of A = 1.25 X mph

Speed = dist/time =>

For A 1.25X = 35+y divide by 7/4 hrs
For B X = y divided by 7/4 hrs

from 1 & 2 we get :

y = 140 miles

putting this in speed equation for A gives 100 miles/hr.

Answer E
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---- Sorry i mistook the speed of A to be 1.5 times of B's speed instead of 1.25 times. I corrected the calculations ------

Since A catches up to B at 1:30pm, they are at the same location at this time.
By 3:15 pm -- 7/4 hours later -- B is behind A by 35 miles, implying that A travels 35 more miles than B in 7/4 hours.
Since A travels 35 more miles than B in 7/4 hours, the DIFFERENCE between A's rate and B's rate = 35/(7/4) = 20 miles per hour.

Since A's rate is 5/4 B's rate, for every 4 miles traveled by B, A travels 5 miles.
Thus, the rate ratio for A and B = 5:4 = 50:40 = 100:80, implying that A's rate = 100 miles per hour and B's rate = 80 miles per hour, for a rate difference of 20 miles per hour.

The correct answer is E.