Hi N2G,
May I ask you why you're not satisfied with the answer? That's exactly how I read it.
This usage of the infinitive is called "
infinitive of purpose" and answers the question "why?"
"We must race against time to overcome all difficulties."
Why must we race against time?
(In order to) overcome all difficultiesCompare:
I went to that shop to buy a skirt.
I had to read that sentence twice to understand it.What would happen if you used "and"? This would change the meaning of the sentence, linking "overcome" to "must":
"We must race against time and overcome all difficulties." What must we do?
no. 1: we must race against time
no. 2: we must overcome all difficultiesHowever, does this make sense? Hmm, I'm not quite sure and leave the question to others.