Question 392018
It takes a crew 1 hour and 30 minutes longer to go 12 miles upstream than to return. Find their rate in still water if the rate of the current is 2mph.
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let speed of boat be x mph
current speed = 2 mph.
upstream speed = x-2 mph
downstream speed = x-2 mph
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time = distance / speed
upstream time -downstream time = 1 1/2 = 3/2 hours
{{{x/(x-2) - x/(x+2) = 3/2}}}
LCD = (x+2)(x-2)
multiply by (x+2)(x-2)
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x(x+2)-x(x-2)/(x+2)(x-2) = 3/2
x^2+2x-x^2+2x/(x+2)(x-2)=3/2
4x/(x+2)(x-2)= 3/2
cross multiply
8x= 3(x+2)(x-2)
8x=3x^2-12
3x^2-8x-12=0
Find roots by quadratic equation
b^2-4ac=208
{{{x1= (8+sqrt(208))/3}}}
x1= 3.73 mph speed of boat.
x2 is negative so ignore
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m.ananth@hotmail.ca