Question 923062
antonio paddles 1 mile upstream and 1 mile back in the total time of 1 hour. The speed of the river is 2 miles per hour. Find the speed of Antonios paddleboat in still water?
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let x=speed of paddleboat in still water
x+2=speed of paddleboat downstream
x-2=speed of paddleboat upstream
travel time=distance/speed
{{{1/(x-2)+1/(x+2)=1}}}
lCd:(x+2)(x-2)
x+2+x-2=(x+2)(x-2)
2x=x^2-4
x^2-2x-4=0
solve for x using quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=1, b=-2, c=-4
{{{x = (2 +- sqrt( 4-4*1*-4 ))/(2*1) }}}
{{{x = (2 +- 2sqrt( 5 ))/(2) }}}
x=1±√5
x≈3.23
speed of Antonios paddleboat in still water? 3.23 mph