The Pacific Crest trail runs from the US border with Mexico

The Pacific Crest trail runs from the US border with Mexico to it\'s border to Canada.the Appalachian trail extends between Springer Mountain in Georgia and the Mount Katahdin in Main. the sum of the lengths of the trails is $4824 miles, the difference is $478miles, and the Pacific Crest trail is the longer.find the length of each trail.write the systems of the equations for the described information.

Solution

Let,

length of  Pacific Crest trail = x miles

length of Appalachian trail trail = y miles

Set up equation as

x +y =4824

x -y =478

Adding both, we get

2x =5302

x=2651

Subsitute 2651 in first equation

2651+y= 4824

y=2173

Therefore,

length of  Pacific Crest trail = 2651 miles

length of Appalachian trail trail = 2173 miles