Question 290001
Rate*Time=Distance
Let's call the speed of the barge S. 
Against the current,
1.{{{(S-4)*T1=63}}}
With the current,
2.{{{(S+4)*T2=63}}}
and we also know
{{{T1+T2=15}}}
From eq. 1 and 2,
{{{T1=63/(S-4)}}}
{{{T2=63/(S+4)}}}
Then,
{{{63/(S-4)+63/(S+4)=15}}}
{{{63(S+4)+63(S-4)=15(S+4)(S-4)}}}
{{{63S+252+63S-252=15(S^2-4S+4S-16)}}}
{{{126S=15S^2-240}}}
{{{15S^2-126S-240=0}}}
{{{5S^2-42S-80=0}}}
You can factor this equation.
{{{(5S+8)(S-10)=0}}}
Two solutions,
{{{5S+8=0}}}
{{{5S=-8}}}
{{{S=-8/5}}}
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{{{S-10=0}}}
{{{S=10}}}
Since we specified the direction of with and against the current, we assumed the barge speed was positive, so we only keep the positive result.
{{{highlight(S=10)}}}