Question 1195643
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Note: Don't put your whole question inside the "{}" symbols; those symbols are supposed to contain only mathematical equations or expressions.<br>
Let x be the speed of the boat in still water. Then x+4 is its speed downstream (with the current) and x-4 is its speed upstream (against the current).<br>
Time to go upstream 6 miles: 6/(x-4)
Time to got downstream 6 miles: 6/(x+4)
The total time is 2 hours:<br>
{{{6/(x-4)+6/(x+4)=2}}}<br>
Multiply by the least common denominator, (x-4)(x+4):<br>
{{{6(x+4)+6(x-4)=2(x^2-16)}}}
{{{12x=2x^2-32}}}
{{{2x^2-12x-32=0}}}
{{{x^2-6x-16=0}}}
{{{(x-8)(x+2)=0}}}
{{{x=8}}} or {{{x=-2}}}<br>
Obviously the negative solution makes no sense, so x=8.<br>
ANSWER: the speed of the boat in still water is 8mph.<br>
CHECK: {{{6/(x-4)+6/(x+4)=6/4+6/12=3/2+1/2=2}}}<br>