Question 983571
<pre>
                speed        time       distance    EQUATIONS
NORMAL           r            t          d          rt=d
FASTER          r+30         t-2.5       d          (r+30)(t-2.5)=d
SLOWER          r-10         t+2.5       d          (r-10)(t+2.5)=d


Additional equation might help:          (r+30)(t-2.5)=(r-10)(t+2.5)
</pre>


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FAST equation
{{{rt+30t-2.5r-75=d}}}
{{{d+30t-2.5r-75=d}}}
{{{30t-2.5r-75=0}}}
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SLOW equation
{{{rt-10t+2.5r-25=d}}}
{{{-10t+2.5r-25=0}}}
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The additional equation in the table is not necessary.


The equations as found can be simplified for convenience if multiply each by 2.
Those as a system of equations:
{{{system(60t-5r-150=0,-20t+5r-50=0)}}}
and then further
{{{system(12t-r-30=0,4t-r+10=0)}}}


Elimination Method is perfectly convenient for the system.
{{{12t-r-30-(4r-r+10)=0-0}}}
{{{8r-30-10=0}}}
{{{8r=40}}}
{{{highlight(highlight(r=5))}}}