Question 416526
{{{x^2 + (x+5)^2  = 25^2}}}
{{{x^2 + x^2 + 10x + 25 = 625}}}
{{{2x^2 + 10x = 600}}}
{{{x^2 + 5x = 300}}}
Complete the square
{{{x^2 + 5x + (5/2)^2 = 300 + (5/2)^2 }}}
{{{ (x + (5/2))^2 = 1200/4 + 25/4 }}}
{{{ (x + (5/2))^2 = 1225/4 }}}
Take the square root of both sides
{{{x + 5/2 = 35/2}}}
{{{x = 30/2}}}
{{{x = 15}}}
{{{x + 5 = 20}}}
The ships are traveling 15 mi/hr and 20 mi/hr
check answer:
{{{x^2 + (x+5)^2  = 25^2}}}
{{{15^2 + (15+5)^2  = 25^2}}}
{{{225 + 400 = 625}}}
{{{625 = 625}}}
OK