Question 886481
The rate of a river's current is 2 mph. A rowing crew can row 10mi down the river and back in 4 hours. Find the rowing rate in calm water.
***
let x=rate of rowoat in calm waters
x+2=rate of rowboat downstream
x-2=rate of rowboat upstream
travel time =distance/rate
{{{10/(x+2)+10/(x-2)=4}}}
lcd:(x+2)(x-2)
10(x-2)+10(x+2)=4(x+2)(x-2)
10x-20+10x+20=4(x^2-4)
20x=4x^2-16
4x^2-20x-16=0
x^2-5x-4=00.70
solve for x by quadratic formula
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=2, b=-20, c=2
ans:
x≈-0.70 (reject)
or 
x≈5.7
rowing rate in calm water≈5.7 mph