Let x be the distance to Horseshoe Lake, in miles.

Then the length of the Crystal palace tour is (2x-0.5) miles, according to the condition.


The condition also says that the sum of two lengths is 3.25 miles, or

x + (2x-0.5) = 3.25.


3x -0.5 = 3.25

3x = 3.25 + 0.5 = 3.75  ====>  x =  = 1.25.


Thus the distance to Horseshoe Lake is 1.25 miles,  and the Crystal palace tour is 2*1.25 - 0.5 = 2 miles long.