Question 1061259
Accounting for time quantities seems like a good way to think this, but not so good trying to see points on a time line.  All we know of time is the sum of their travel times.
<pre>
PERSON           SPEED           TIME        DISTANCE
Thaddeus          30              t
Ian               35              i
Total                             11           355


PERSON           SPEED           TIME        DISTANCE
Thaddeus          30              t            30t
Ian               35              i            35i
Total                             11           355
</pre>


{{{t+i=11}}}
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Distance sum, {{{30t+35i=355}}}
{{{6t+7i=71}}}
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Solve this system for the times, t and i:
{{{system(t+i=11,6t+7i=71)}}}.
Use the Elimination Method.