Question 1153877
<pre>
                   SPEED         TIME           DISTANCE

TRAIN              r+40          120/(r+40)       120

CAR                r             120/r            120

DIFFERENCE                      {{{1/2}}}
</pre>
Thirty minutes is one-half hour.


The train's time is less than car's time by half hour.

{{{120/r-120/(r+40)=1/2}}}.
Solve for r+40.
(But can be arranged differently.)

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{{{240/r-240/(r+40)=1}}}

{{{240(r+40)-240r=r^2+40r}}}

{{{240r+240*40-240r=r^2+40r}}}

{{{240*40=r^2+40r}}}

{{{r^2+40r-40*240=0}}}

{{{r^2+40r-9600=0}}}

{{{(r-80)(r+120)=0}}}.

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