Question 1010958
{{{system(r=unknownUsualSpeed,t=unknownUsualTime,h=2,k=20,d=800)}}}

<pre>
          rate      time       distance
IF        r+k       t-h         d
USUAL     r          t          d
</pre>

System of equations to solve for t and r:
{{{system((r+k)(t-h)=d,rt=d)}}}


STEPS FOR SOLVING - ARITHMETIC
{{{rt+kt-hr-kh=d}}}
substitute for d using "usual" equation;
{{{rt+kt-hr-kh=rt}}}
{{{kt-hr-kh=0}}}
{{{t=(hr+kh)/k}}}

Again use the "usual" equation, now substituting for t.
{{{r(hr+kh)/k=d}}}
{{{r(hr+kh)=kd}}}
{{{hr^2+khr=kd}}}
{{{highlight_green(hr^2+khr-kd=0)}}}------almost to a formula for r.   You can decide when you want to 
make the substitutions for the given values.  Continue symbolically from here and substitute later,
or do the substitutions now, and continue the arithmetic either way.
-


Substituting now,  and get
after simplifying,
{{{r^2+20r-8000=0}}}


Formula for general solution of quadratic equation gives {{{highlight(r=80)}}}.