speed= distance/time so, letting d be the distance between the two towns, in miles, and t be the time, in hours, for the trip, 32= d/t.

If"it had gone 4mph faster" its speed would have been 32+ 4= 36 and "it could have made the trip in 1/2 hr less time" so the time would be t- 1/2. Now "speed= distance/time" so 36= d/(t+1/2).

32= d/t is the same as d= 32t.

36= d/(t+1/2) is the same as d= 36(t+1/2)= 36t+ 18.

d= 32t= 36t+ 18.

Solve 32t= 36t+ 18 for t and then use d= 32t to find the distance between the towns.