Question 964015
Use the formula, rate * time = distance
Set x = speed in still water
(x-2) * t1 = 6 miles
(x+2) * t2 = 6 miles
t1, the time paddling upstream  = distance 6 miles/ rate (x-2) or
6/(x-2)
t2, the time paddling downstream  = distance 6 miles/ rate (x+2) or
6/(x+2)
t1 + t2 = 4 hours, so
6/(x-2) + 6/(x+2) = 4
A common denominator is (x-2)(x+2) so we want
{{{6/(x-2)*(x+2)/(x+2) + 6/(x+2)*(x-2)/(x-2) = 4}}}
expanding
{{{(6x + 12 + 6x -12)/(x^2-4) = 4/1}}}
simplify
{{{(12x)/(x^2-4) = 4/1}}}
do cross products
{{{12x=4(x^2-4)}}}
{{{12x=4x^2-16}}}
{{{0=4x^2-12x-16}}}
divide by 4
{{{0=x^2-3x-4}}}
factoring
{{{0 = (x-4)(x+1)}}}
So possible values for x are 4 and -1
Since we need a positive speed, the speed in
still water is 4 mph