SOLUTION: a woman cycles 8 mi/h faster than she runs.every morning she cycles 4mi and run 2and1/2 mi for a total of a one hour workout. how fast does she run

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: a woman cycles 8 mi/h faster than she runs.every morning she cycles 4mi and run 2and1/2 mi for a total of a one hour workout. how fast does she run      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 973734: a woman cycles 8 mi/h faster than she runs.every morning she cycles 4mi and run 2and1/2 mi for a total of a one hour workout. how fast does she run
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
a woman cycles 8 mi/h faster than she runs.every morning she cycles 4mi and run 2and1/2 mi for a total of a one hour workout. how fast does she run.
***
let x=running speed
x+8=cycling speed
Travel time=distance/speed
%285%2F2%29%2Fx%2B4%2F%28x%2B8%29=1
lcd:x(x+8)
%285%2F2%29%28x%2B8%29%2B4x=x%5E2%2B8x
(mult. by 2)
%285x%2B40%29%2B8x=2x%5E2%2B16x
2x^2+3x-40=0
solve for x by quadratic formula:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a=2, b=3, c=-40
ans: x≈3.78
how fast does she run? 3.78 mph