Let A and B be the charges for respective companies.
A=20+0.59k, B=16+0.63k where k is the distance in km.
(i) When A=B, 20+0.59k=16+0.63k, 4=0.04k, k=100km (as you thought), so the charge is 20+59=$79=16+63.
(ii) When A<B (A is the better choice because it's cheaper) 20+0.59k<16+0.63k, 4<0.04k, 100<k, so, when the distance is less than 100km, A is the better choice.