Question 872087
The current river flows at the rate of 4mph. In order for a boat to travel 24 miles up river and then return in a total of 5 hours how fast must the boat be able to travel in still water?
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let x=speed of boat in still water
x+4=speed of boat downstream
x-4=speed of boat upstream
travel time=distance/speed
..
24/(x+4)+24/(x-4)=5
24(x-4)+24(x+4)=5(x+4)(x-4)
24x-96+24x+96=5(x^2-16)
48x=5x^2-80
5x^2-48x-80=0
solve for x by quadratic formula:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
a=5, b=-48, c=-80
ans:
x≈-1.45(reject)
or
x≈11.05
speed of boat in still water≈ 11.05 mph