Question 759443
felix rode 18 miles downstrem and back to the same place where he started, in 3 hours and 12 minutes. find the rate of felix in still water if the velocity of the stream is 3 miles per hour.
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let x=rate of Felix in still water
x+3=rate downstream
x-3=rate upstream
travel time=distance/rate
3hr and 12 min=16/5 hrs
{{{18/(x+3)+18/(x-3)=16/5}}}
LCD:5(x+3)(x-3)
{{{5*18*(x-3)+5*18*(x+3)=16(x-3)(x+3)}}}
{{{90x-270+90x+270=16x^2-144}}}
16x^2-180x-144=0
4x^2-45x-36=0
(4x+3)(x-12)=0
x=-3/4 (reject, x>0)
or
x=12
rate of Felix in still water=12 mph