It takes 40 minutes more going up or 40/60 = 0.67 hours
more.
Let us say that:
t = the time required for him running down
t + 0.67 = time required for him running up
Since the distance of running up and down must be equal
therefore:
(3 miles / hr) * (t + 0.67) = (5 miles / h) * t
3 t + 2.01 = 5 t
2 t = 2.01
t = 1.005 hr
So the total length of the hike is:
length = 2 * (5 miles / hr) * (1.005 hr)
length = 10.05 miles
