<PRE><B>Question 900249</B>
Be aware:  I likely made a mistake in this, and have not successfully finished solving....


RT=D uniform rates for travel


_____________speed_______time______distance
IF FASTER____r+3_________t-2/3_____d=(r+3)(t-2/3)
IF SLOWER____r-2_________t+2/3_____d=(r-2)(t+2/3)
Rate Used____r____________t________d=rt


 A possible place in the analysis that someone could become stuck is to not recognize the very simple r*t=d, while each of these three variables is still unknown.  


(Removed the previous shown solution because of continuing mistakes while making corrections.  See the following.)



***CONTINUING WITH GOOD SOLUTION PROCESS---------------------------------------------------------


FAST
{{{rt+3t-(2/3)r-2=d}}}
{{{rt+3t-(2/3)r-2=rt}}}
{{{3t-(2/3)r-2=0}}}
{{{9t-2r-6=0}}}
{{{highlight_green(9t-2r=6)}}}


SLOW
{{{rt-2t+(2/3)r-4/3=d}}}
{{{-2t+(2/3)r-4/3=0}}}
{{{2t-(2/3)r+4/3=0}}}
{{{6t-2r+4=0}}}
{{{3t-r+2=0}}}
{{{highlight_green(3t-r=-2)}}}


Start with Elimination Method to eliminate r.
Multiply SLOW equation by 2 and use  subtraction, {{{FAST-SLOW}}}.
{{{9t-2r-(6t-2r)=6-(-4)}}}
{{{9t-2r-6t+2r=10}}}
{{{3t=10}}}
{{{highlight(t=10/3=3&amp;1/3)}}}, hours


Use t in either equation, here being SLOW as the chosen equation, to find r.
{{{-r+3(10/3)=-2}}}
{{{-r+10=-2}}}
{{{-r=-12}}}
{{{highlight(r=12)}}}, miles per hour


The distance, according to r*t?
40 miles.
</PRE>