Question 997917
<pre>
                     rate       time         distance

WORK, TRAFFIC        {{{r[w]}}}       {{{d/r[w]}}}           d

HOME, FASTER         {{{r[h]}}}       {{{d/r[h]}}}           d

Total                            t
</pre>


The description means that these variable values are assigned:
{{{system(r[w]=30,r[h]=40,t=4&1/2)}}}.  


The unknown variable in the whole description is d, the distance each way between work and home.  The time sum equation will be what to use to solve for d.


{{{highlight(d/r[w]+d/r[h]=t)}}}


{{{d(1/r[w]+1/r[h])=t}}}

{{{d=t/(1/r[w]+1/r[h])}}}

{{{d=t/((r[h]+r[w])/(r[w]r[h]))}}}

{{{highlight(d=(r[w]r[h]t)/(r[w]+r[h]))}}}


You solve for d, distance each way, but not yet solved for time each way.  Just use the expressions shown in the data table, substitute for d and for the given rates, and evaluate each time value.