The Two Cities

A traveler goes from city $A$ to city $B$.

When traveling uphill, he moves at speed $u$ km/h
When traveling on flat road, he moves at speed $f$ km/h
When traveling downhill, he moves at speed $d$ km/h
(Of course $0<u<f<d$)

To go from $A$ to $B$, it takes $T_1$ hours.
To go from $B$ to $A$, it takes $T_2$ hours.


For some triples $(u,f,d)$ these information are sufficient to determinate the distance between $A$ and $B$
(For instance $(30,35,42)$)

How many such triples of positive integers $(u,f,d)$ with $GCD(u,f,d)=1$ are there if $d<{10}^8$?

[My timing: 40 sec]
All values in this problem (speed or distance) are assumed to be integers.