Mr. brown drove from his home to his school at the rate of 25 mph and returned by a different route at the rate of 30 mph. the route by which he returned was 5 miles longer than the route by which he went. the return trip took 10 minutes less than the trip out. find the distance mr. brown traveled each way.

If we let
x and t1 as the distance traveled and the travel time, respectively using the first route
y and t2 as the distance traveled and the travel time, respectively using the second route

Then we have the equations:
x = 25 t1
y = 30 t2
y = x + 5
t2 = t1 - 10/60

Solving of x, y, t1 and t2
x = 50 mi
y = 55 mi
t1 = 2 hr
t2 = 1.83 hr