SOLUTION: The Caverns of Sonora have two different tours: Crystal palace and horseshoe lake. Total length of the two tours is 3.25 miles. Crystal is a half mile less than twice the distance

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Question 1116606: The Caverns of Sonora have two different tours: Crystal palace and horseshoe lake. Total length of the two tours is 3.25 miles. Crystal is a half mile less than twice the distance of Horseshoe Lake. Determine the length of each tour.
My son and I have been struggling trying to show work for this problem - can you please help??
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.
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 = 3.75%2F3 = 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.

Solved.