Question 987007
More general:
A Johnson motorboat goes {{{d[u]}}} miles upstream in the same time it requires to go {{{d[d]}}} miles downstream. If the river flows at <i>s</i> mph, find the speed <i>r</i> of the boat in still water.

<pre>
Direction         rate     time    distance
upstream          r-c       t      {{{d[u]}}}
downstream        r+c       t      {{{d[d]}}}


Direction         rate       time    distance
upstream          r-c       {{{d[u]/(r-c)}}}      {{{d[u]}}}
downstream        r+c       {{{d[d]/(r+c)}}}      {{{d[d]}}}
</pre>



The time quantities were described as equal.
{{{highlight_green(d[u]/(r-c)=d[d]/(r+c))}}}
Their reciprocals are also equal (not the only strategy)...
{{{(r-c)/d[u]=(r+c)/d[d]}}}

{{{(r-c)d[d]=(r+c)d[u]}}}

{{{r*d[d]-c*d[d]=r*d[u]+c*d[u]}}}

{{{rd[d]-rd[u]=cd[u]+cd[d]}}}

{{{r(d[d]-d[u])=cd[u]+cd[d]}}}

{{{highlight(r=(cd[u]+cd[d])/(d[d]-d[u]))}}}


Evaluate the boat speed r according to
{{{system(d[u]=5,d[d]=7,c=2)}}}.