Question 1033445
Use a time line instead of time points.  Your trains seem described as traveling
in opposite directions and moving toward each other.

RT=D is a basic travel rates rule connecting RATE, TIME, DISTANCE.

<pre>
VEHICLES        RATE      TIME      DISTANCE
---------------------------------------------
Case1
A                r        2+1
B                s         2
Total                                 216
---------------------------------------------
Case2
A                r        3/2
B                s        3
Total                                 216
---------------------------------------------</pre>


Time values can be found without putting them as variables.  The two unknown variables
are FirstTrain at rate r and SecondTrain at rate s.  Each situation uses time span of
three hours, but case 1 is when train number two travels less time; and case 2 is when
first train travels less time.  Think and review the data table before continuing...


-----to continue, fill-in the distance expressions.

<pre>
VEHICLES        RATE      TIME      DISTANCE
---------------------------------------------
Case1
A                r        2+1        r*3
B                s         2          s*2
Total                                 216
---------------------------------------------
Case2
A                r        3/2        r*(3/2)
B                s        3          s*3
Total                                 216
---------------------------------------------</pre>


{{{highlight(system(3r+2s=216,3r/2+3s=216))}}}
Solve this system for r and s, the speeds of FirstTrain and SecondTrain.