SOLUTION: Driving down a mountain, Tom finds that he has descended 1800 feet in elevation by the time he is 3.25 miles horizontally away from the top of the mountain. Find the slope of his d

Algebra ->  Algebra  -> Customizable Word Problem Solvers  -> Travel -> SOLUTION: Driving down a mountain, Tom finds that he has descended 1800 feet in elevation by the time he is 3.25 miles horizontally away from the top of the mountain. Find the slope of his d      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com
Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 42109This question is from textbook Begining Algebra
: Driving down a mountain, Tom finds that he has descended 1800 feet in elevation by the time he is 3.25 miles horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth.This question is from textbook Begining Algebra

Answer by psbhowmick(489) About Me  (Show Source):
You can put this solution on YOUR website!
Tom travels down an inclened (as he is descending a mountain).
So let Tom travel from C to A along CA.
C is the point where he begun his journey and A is the point where he finds that he has traveled 3.25 miles horizontally (AB = 3.25 mi) and has descended 1800 ft vertically (CB = 1800 ft).

See this triangle ABC.
drawing%28400%2C100%2C-5%2C195%2C-5%2C25%2C%0D%0Alocate%280%2C0%2CA%29%2C%0D%0Alocate%28171.6%2C0%2CB%29%2C%0D%0Alocate%28171.6%2C18%2CC%29%2C%0D%0Aline%280%2C0%2C171.6%2C0%29%2C%0D%0Aline%280%2C0%2C171.6%2C18%29%2C%0D%0Aline%28171.6%2C0%2C171.6%2C18%29%0D%0A%29

1 mile = 5280 ft.
So 3.25 miles = 3.25 x 5280 = 17160 ft.

Here, AB = 3.25 miles = 17160 ft and BC = 1800 ft.
Therefore slope = BC%2FAB = 1800%2F17160 = 15%2F143 = 0.10 (approximate to nearest hundredth).