Question 183638
This is a speed and distance problem. The assumption here is the speed of the sailboat is the same in both direction. The current however will help travel downstream and low travel upstream. The distance travelled in each direction will be the same.
{{{d=s*t + c*t}}} where s=speed of sailboat and c=speed of current
downstream would be
{{{20 = s*3 + c*3}}}
coming back upstream
{{{20 = s*4 - c*4}}}
If we solve the second equation for s we get
{{{20 + 4c = 4s}}}
Divide both sides by 4
{{{20/4 + 4c/4 = 4s/4}}}
Simplify
{{{5+c=s}}}
Using substitution, replace s with 5+c in first equation
{{{20 = 3(5+c)+3c}}}
Distribute to remove parenthesis
{{{20=15+3c+3c}}}
Move constants to one side and combined like variables
{{{20-15=6c}}}
{{{5=6c}}}
divide both sides by 6
{{{5/6=6c/6}}}
{{{c=5/6}}}mph
Put this value for c back into s=5+c
{{{s=5+5/6}}}mph