If a taxi charges $3.50 for the first on-fifth of a mile, then $0.55 cents for each additional one-fifth mile, how far can one travel for $13.95?

Let's forget for the tie being the cost ($3.5)of the 1st fifth of a mile:

Taxi charge excluding $3.5, is $13.95 - $3.5 = $10.45.

If each of the 5th (1/5) of a mile costs $0.55, then with $10.45 we can drive:
10.45/0.55 = 19 fifth of a mile. Add to that the 1st fifth = 20 fifth of a mile
 20 fifth = 20 x 1/5 = 4 miles (answer)