Question 156479
Distance(d) equals Rate(r) times Time(t) or d=rt;  r=d/t and t=d/r

let r=rate (speed) of boat in still water
time to travel upstream=45/(r-3)
time to travel downstream=45/(r+3)

And we are told that the above two times add up to 8 hours, so:

45/(r-3)+45/(r+3)=8  multiply each term by (r-3)(r+3)
45(r+3)+45(r-3)=8(r-3)(r+3) get rid of parens

45r+135+45r-135=8r^2-72 or
90r=8r^2-72  subtract 90r from each side

90r-90r=8r^2-90r-72 and
8r^2-90r-72=0  quadratic in standard form.  Solve using the quadratic formula:
{{{r = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{r = (90 +- sqrt((-90^2)-4*8*(-72) ))/(16) }}} 
{{{r = (90 +- sqrt(10404))/(16) }}} 
{{{r = (90 +- 102)/(16) }}} 
{{{r = (90 + 102)/(16) }}} 
{{{r = (192)/(16) }}}
{{{r=12}}} mph-----------------------------------ans
and
{{{r = (90 - 102)/(16) }}}
{{{r=-12/16}}}-------------------NO GOOD----IN THIS PROBLEM, SPEED IS POSITIVE

CK
45/(12-3)+45/(12+3)=8
45/9 +45/15=8
5+3=8
8=8


Hope this helps---ptaylor