Verb conjugation of "conquistar" in Spanish

I ordered a cab at four o'clock in the morning which took me to the Central Bus Station. I was much to early because the bus would go just at seven o'clock. Anyway I was sitting there and listening to music.
The climb was much exhausting than I had presumed. I had forgotten that we were at high altitude where there is less oxygen and that every step required double effort. It was a great exercise.
The same day that I gave my last presentation about our pilot project I flew away. The first lag was NYC's airport John F. Kennedy. I left Europe after midnight and arrived there at five o'clock, more or less.