You hike up a mountain trail at a rate of 1/4 mile every 10 minutes. you hike 5 miles every 2 hours on the way down the trails. How much further do you hike in 3 hours on the way down the hill than in 3 hours on the way up?
On the way up, you hike at a rate of 1/4 mile every 10 minutes. In 3 hours, there are 3 * 60 = <<3*60=180>>180 minutes.
So on the way up, you would hike a total of 180 / 10 * 1/4 = <<180/10*1/4=4.5>>4.5 miles.
On the way down, you hike 5 miles every 2 hours, which means you hike 5 / 2 = <<5/2=2.5>>2.5 miles every hour.
Therefore, in 3 hours on the way down, you would hike a total of 3 * 2.5 = <<3*2.5=7.5>>7.5 miles.
Therefore, you would hike 7.5 - 4.5 = <<7.5-4.5=3>>3 miles further on the way down than on the way up. Answer: \boxed{3}.