There is a slight difference in your sentence between what you mean and what you write. Unfortunately, this is an important one. When you say:

On her free time she likes to ski, travel and fast cars.

We can translate that, literraly, in:

Pendant son temps libre elle aime skier, voyager, et les voitures rapides.

Which translate back in English to:

On her free time she likes skiing, travelling and cars which are fast.

In French, a lot of verbs can be used without particles. For example, “faire du ski” refers as “skier”, while “faire du voyager” refers as “voyager”. Fast is not a verb in French, not as intended here (I guess), but an adjective, used to describe something. A fast car is a car which is fast.

In English (thanks @Aaron), fast as a verb means “to not eat for a certain period of time”, and refers in French as “Jeûner”. (Ramadan, for example).

(I feel you, when learning english earlier I had a rough time figuring out “a red car”, which is “une voiture rouge” (a car red) in French).

If you want to say she likes driving fast cars during her free time, you could say:

In her free time she likes skiing, travelling, and driving fast cars.

Which translates to:

[Pendant / Durant / Lors de] son temps libre, elle adore skier, voyager, et conduire des voitures rapides.