Question 996067
A traveler travels {{{d}}} miles downstream in {{{t[d]}}} hour. the return trip takes {{{t[u]}}} hours.Write the equations to solve the problem. what's the rate of the boat in still water?

<pre>
Let c be the rate of the current; r is the rate for the boat if no current.
The use of the subscripts are d for DOWNSTREAM and u for UPSTREAM.

             speed       time       distance
TO           r+c        {{{t[d]}}}        d
FROM         r-c        {{{t[u]}}}        d


Note that the unknown variables in the problem description are r and c.
</pre>
{{{system((r+c)*t[d]=d,(r-c)*t[u]=d)}}}, the starting system of equations.


{{{r*t[d]+c*t[d]=d}}}
{{{c*t[d]=d-r*t[d]}}}
{{{c=(d-rt[d])/t[d]}}}


{{{rt[u]-ct[u]=d}}}
{{{rt[u]-((d-rt[d])/t[d])t[u]=d}}}
{{{rt[u]*t[d]-(d-rt[d])t[u]=d*t[d]}}}
{{{rt[u]*t[d]-d*t[u]+rt[d]t[u]=d*t[d]}}}
{{{rt[u]t[d]+rt[d]t[u]-dt[u]=dt[d]}}}
{{{rt[u]t[d]+rt[u]t[d]=dt[d]+dt[u]}}}
{{{r(2t[u]t[d])=dt[d]+dt[u]}}}
{{{highlight(r=(dt[d]+dt[u])/(2t[u]t[d]))}}}------answer in symbolic form.