my best run for this was exactly 1h 03m 47s (with Purna) so you can do it really fast, here are my Tipps:
1. Run like hell, only fight if you have to, kill every Infected you see and don't try to bother with Thugs.
2. get yourself Rage Mode early, you gonna need it in two places: 1. when you get the juice, in the shack where there are 2 thugs and 4 Walkers. 2. in the swimming pool Room of the hotel.
3. get yourself while doing other Quests 3 Food rations, there are two in a bar near the Life Guard, and one in the first Gas Station.
4. practice Driving and do the Quest where you get the Car at the Life guard first.
5. when you fall down, you can press A and back(evasive move backwards) before you reach the ground, you will take no Damage doing so, this trick allows you to take several Shortcuts.
6. RUN LIKE HELL!!!!
hope this helps :)