Ahigh school student in seattle, washington, attends the university of central florida. on the way to ucf he took a southern route. after graduation he returned to seattle via a northern trip. on both trips he had the same average speed. if the southern trek took hours, the northern trek took hours, the northern trek was miles longer, how long was each trip?

If the southern trek took 48 hours and the norther trek took 53 hours, the northern trek was 285 miles longer than the southern trek , how long was each trek.
If we assume the distance of the southern route was d , then the northern route will be d+285. 
Speed is given by distance/ time 
Hence, speed through the southern route will be d/48 and through the northern route will be (d+285)/53.
But in both routes the speed was the same.
Therefore, d/48= (d+285)/53. Solving for d
                     53 d= 48 (d +285)
                      53d = 48d +13680
                          5d=13680
                             d= 2736  and (d+285= 3021)
There, the southern route is 2736 miles long and the northern route is  3021 miles long