Question 1058617
The description is constant travel rates problem, and not necessarily a rational equations problem.

<pre>
             SPEED        TIME      DISTANCE

LOADED       r             t          d

EMPTY       r+15          t-1.5       d

TOTAL
</pre>


{{{system(rt=d,(r+15)(t-1.5)=d)}}}


{{{t=d/r}}}
-
{{{(r+15)((d/r)-1.5)=d}}}
{{{r(r+15)(d/r-1.5)=d}}}
{{{(r+15)(d-1.5r)=d}}}
{{{rd+15d-1.5r^2-(15)(1.5)r=d}}}
{{{rd+14d-1.5r^2-22.5r=0}}}
{{{-rd-14d+1.5r^2+22.5r=0}}}
{{{1.5r^2-rd+22.5r-14d=0}}}
{{{1.5r^2+(22.5-d)r-14d=0}}}-----quadratic equation in r, but also d is still unknown variable.


{{{r=(d-22.5+- sqrt((22.5-d)^2-4*1.5*(-14d)))/3}}}


{{{r=(d-22.5+- sqrt((22.5-d)^2+84d))/3}}}


{{{r=(d-22.5+- sqrt(506.25-45d+d^2+84d))/3}}}


{{{highlight(r=(d-22.5+- sqrt(d^2+39d+506.25))/3)}}}
The discriminant is not a perfect square, and you do not have enough information described to know the value of d.
This is all that can be done.