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.
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let x=running speed
x+8=cycling speed
Travel time=distance/speed
{{{(5/2)/x+4/(x+8)=1}}}
lcd:x(x+8)
{{{(5/2)(x+8)+4x=x^2+8x}}}
(mult. by 2)
{{{(5x+40)+8x=2x^2+16x}}}
2x^2+3x-40=0
solve for x by quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=2, b=3, c=-40
ans: x≈3.78
how fast does she run? 3.78 mph