You are correct that past consideration is no consideration; however, there is an exception to this rule which may be applicable to your scenario.
In your argument you may should first define consideration by using Currie v Misa (1875) L wherein Lush J stated, ‘A valuable consideration, in the sense of the law, may consist either in some right, interest, profit, or benefit accruing to the one party, or some forbearance, detriment, loss, or responsibility, given, suffered, or undertaken by the other.’ You can back this up by Lord Dunedin's pronouncement in Dunlop Pneumatic Tyre Co. Ltd v Selfridge & Co Ltd.
Also, consider the doctrine of implied assumpsit - i.e. that performance of a past act at the request of the party who subsequently implies to pay for it may be good consideration (in other words, that the driver would not have helped if the broken-down driver did not request it) , despite the promise not arising contemporaneously (see, for example, Lampleigh v Brathwaite). In order to demonstrate this, three things must be present: (i) that the promisee performed the act at the request of the other party; (i) that it was implicit that the promisee would be rewarded for performing the act; and (iii) that the promise, had it been made in conjunction with the act, would have been enforceable in law (Pao On v Lau Yiu Long and Re Casey's Patents, Stewart v Casey ). For example, in Lampleigh v Brathwaite, although the promise arose after the performance, the consideration was proceeded by a request, meaning that consideration was valid.
However, a gratuitous promise made at the promissor's own volition would not render a subsequent promise as good consideration; the promise to remunerate the driver for towing the car into town for an act which he had already performed before the promise is made would only be good consideration if the doctrine of implied assumpsit applies. You should consider Roscorla v Thomas & Re McArdle and argue whether or not the promise was good consideration despite it not arising contemporaneously (apply the doctrine of implied assumpsit, Lampleigh and Pao on v Lau Yiu Long).