I bought a used road bike (07 Trek 2.1) with original tires. The tire says 120 PSI max. pressure. When I tried to pump it with a new hand pump, it went as far as 75 to 80 and couldn't get it inflated anymore. I mean I was pumping a lot and pretty hard, short of killing myself. And I didn't want to damage the tires too. Is this the right pressure? Or should I try to try to get it closer to 120, if so, how?