SOLUTION: There are two different tours for a cave. The Palace tour and the lake tour. The Total length of both tours is 3.25 miles. The palace tour is a half-mile less than twice the distan

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: There are two different tours for a cave. The Palace tour and the lake tour. The Total length of both tours is 3.25 miles. The palace tour is a half-mile less than twice the distan      Log On


   

Question 940847: There are two different tours for a cave. The Palace tour and the lake tour. The Total length of both tours is 3.25 miles. The palace tour is a half-mile less than twice the distance of the Lake Tour. Determine the length of each tour.
1. how do i write an equation for this.
2. How do i solve it.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +P+ = Palace tour in miles
Let +L+ = lake tour in miles
---------------------
(1) +P+%2B+L+=+3.25+
(2) +P+=+2L+-+.5+
---------------------
Substitute (2) into (1)
(1) +2L++-+.5+%2B+L+=+3.25+
(1) +3L+=+3.75+
(1) +L+=+1.25+
and
(2) +P+=+2%2A1.25+-+.5+
(2) +P+=+2.5+-+.5+
(2) +P+=+2+
------------------
The lake tour is 1.25 mi
The Palace tour is 2 mi
------------------------
check:
(1) +P+%2B+L+=+3.25+
(1) +2+%2B+1.25+=+3.25+
(1) +3.25+=+3.25+
OK