Question 147172
{{{d=rt}}} Start with the distance-rate-time formula.



{{{104=(20+r)*t}}} Plug in {{{d=104}}} and {{{r=20+r}}}. Let's call this equation 1.



{{{104/(20+r)=t}}} Divide both sides by {{{20+r}}} to isolate t



So {{{t=104/(20+r)}}}



{{{d=rt}}} Go back to the distance-rate-time formula



{{{56=(20-r)*t}}}  Plug in {{{d=56}}} and {{{r=20-r}}}. Let's call this equation 2.




{{{56=(20-r)*(104/(20+r))}}} Plug in {{{t=104/(20+r)}}}



{{{56(20+r)=104(20-r)}}} Multiply both sides by {{{20+r}}}



{{{1120+56r=2080-104r}}} Distribute.



{{{56r=2080-104r-1120}}} Subtract {{{1120}}} from both sides.



{{{56r+104r=2080-1120}}} Add {{{104r}}} to both sides.



{{{160r=2080-1120}}} Combine like terms on the left side.



{{{160r=960}}} Combine like terms on the right side.



{{{r=(960)/(160)}}} Divide both sides by {{{160}}} to isolate {{{r}}}.



{{{r=6}}} Reduce.



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Answer:


So the answer is {{{r=6}}}



This means that the speed of the river is 6 mph