determine the length of tour

Question

the caverns of Sonora have two different tours. the crystal palace tour and the horseshoe tour; The total length of both tours is 3.25 miles.  The crystal tour is a half-mile less than twice the distance of the horseshoe tour.  Determine the length of each tour.

Answer 1

Let c = crystal palace tour length
Let h = horseshoe tour length

c + h = 3.25
c = 2h - 0.5

using substitution
2h - 0.5 + h = 3.25
3h - 0.5 = 3.25
3h = 3.75
h = 1.25

c = 2h-0.5 = 2.5-0.5 = 2

crystal palace tour is 2 miles
horseshoe tour is 1.25 miles