Question 23019
Let x = speed of the current
15 +x = speed of the boat downstream (with the current)
15-x = speed of the boat upstream (against the current)
Distance upstream = Distance downstream = 36 miles


D=RT
T= D/R


Total Time = D/R + D/R = 5 hours
{{{36/(15+x) + 36/(15-x) = 5}}}


Multiply both sides of the equation by the LCD which is (15+x)(15-x):
{{{(15+x)(15-x)*(36/(15+x)) + (15+x)(15-x)*36/(15-x) = 5*(15+x)(15-x)}}}
{{{36(15-x) + 36(15+x) = 5(225-x^2)}}}
{{{ 540 - 36x + 540 + 36x = 1125 - 5x^2}}}
{{{1080 = 1125 - 5x^2}}}
{{{1080-1125 = -5x^2}}}
{{{-45 = -5x^2}}}
{{{x^2=9}}}
x= 3 or x= -3


Reject the negative answer.  x=3 mph = speed of the current.


R^2 at SCC