Question 864811
the current of a stream moves at 5 mph. a boat travels 31 mi upstream and 31 mi down stream in a total time if 20 hours what is the speed of the boat in still water?
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let x=speed of boat in still water.
x+5=speed of boat downstream.
x-5=speed of boat upstream.
travel time=distance/speed
{{{31/(x+5)+31/(x-5)=20}}}
LCD:(x+5)(x-5)
{{{31(x-5)+31(x+5)=20(x-5)(x+5)}}}
{{{31x-155+31x+155=20(x^2-25)}}}
{{{62x=20x^2-500)}}}
20x^2-62x-500=0
10x^2-31x-250=0
solve for x by quadratic formula: {{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
a=10, b=-31, c=-250
ans:
x≈6.78
speed of the boat in still water? 6.78 mph