As-Salamu ‘alaykum wa rahmatullaahi wa barakaatuh,
I have a car which I drive to work and to the mosque. Sometimes I run across women of my acquaintance and I would like to offer them a ride but I remember that the Prophet, sallallaahu ‘alayhi wa sallam, said: "No person should be alone with a woman except with a mahram." Then, another tradition occurs to my mind; the Prophet, sallallaahu ‘alayhi wa sallam, also said: “And Allaah helps the slave as long as the slave helps his brother.”
How can I reconcile the implications of the two narrations?

All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His Slave and Messenger.

The narration that you referred to is an authentic Hadeeth (narration) that was reported by Al-Bukhari and Muslim . Muslim cited it with the following wording: The Prophet, sallallaahu ‘alayhi wa sallam, said: "No person should be alone with a woman except if there is a Mahram (non-marriageable male) with her." [Muslim]

Hence, according to the general indication of the previously mentioned narration, a Muslim man must not be alone in private with a non-Mahram woman without the presence of one of her Mahram men; since such an act has evil repercussions and might lead to committing sins. Moreover, the second narration that you have mentioned in which the Prophet, sallallaahu ‘alayhi wa sallam, said: “And Allaah helps the servant  as long as the servant helps his brother” is also an authentic Hadeeth. However, there is no contradiction between the two narrations, since the necessary help that was mentioned in the latter is conditional on not leading to committing anything that is forbidden, or else it would be prohibited as well. Allaah The Exalted Says (what means): {“…do not cooperate in sin and aggression.”} [5:2]

Allaah Knows best.