If they immediately ran in opposite directions with speeds of 180 feet per minute and 120 feet per minute respectively, how many minutes would pass before they were 2,420 feet apart?

This is like half the question, but I guess you got the important stuff down...lol. Anyways, the runners run for the same amount of time.  They both stop when the distance between them in 2420, so the thing that's different is their rates, which means that the one that runs faster goes farther than the one that runs slower.  But we don't know the distance they each run, so we can call the distance the faster guy runs "d" and the other distance "2420-d".  Rates are 120 and 180, respectively.  Since d = rt and the time is the same for both, we solve for t to get that t = d/r.  Set up the ratios and cross multiply to solve for d: and 180d=290400-120d.  300d=290400 and d = 968.  Go back to your original equation of d=rt and sub in the d of 968 to solve for t: d=120t so 968=120t and t = 8.06 minutes.

Wow. that is a really cool question.