Two families are vacationing together, driving in separate cars. the harris family averages 45 mph, leaving hometown 6 minutes ahead of the arlen family, who averages 58 mph. how long will it take the arlen family to overtake the harris family

Let x = amount of time the Arlen family must catch up to overtake the Harris family

In principle, the Harris and the Arlen family should cover the same distance. Since distance is speed x time,

45 (6+y) = 58y

270 + 45y = 58y

58y - 45y = 270

y = 270 : 13

y = 20.77min