A high 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 47 hours, the northern trek took 52 hours,

the northern trek was 310 miles longer, how long was each trip?

:

Let d = the southern distance

then

(d+310) = the northern distance

:

Write a speed equation. Speed = dist/time

:

Northern speed = southern speed

=

Cross multiply

52d = 47(d+310)

52d = 47d + 14750

52d - 47d = 14750

d = 14750/5

d = 2,914 mi is the southern route

then

2,914 + 310 = 3,224 mi is the northern route

;

:

We can confirm this by finding the speeds, they should be equal

2914/47 = 62 mph

3224/52 = 62 mph