Question

Please help!!!!!!!
A river flows at the rate of 2mph. If a barge travels 3 miles upstream and back in two hours, what is the speed of the barge in still water?

Answer 1

Let s be the speed of the barge in still water.
Then the speed upstream is (s - 2) mph and the speed downstream is (s + 2) mph.
\[time=\frac{distance}{speed}\]
Time to travel upstream is
\[\frac{3}{s-2}\ hours\]
Time to travel downstream is
\[\frac{3}{s+2}\]
Total time to travel upstream 3 miles and return is 2 hours. Therefore
\[2=\frac{3}{s-2}+\frac{3}{s+2}\]
\[2=\frac{3(s+2)+3(s-2)}{s ^{2}-4}..............(1)\]
Equation (1) can be rearranged to give the quadratic
\[2s ^{2}-6s-8=0...........(2)\]
Now solve the quadratic to find s.