Question 763010
Let r = speed going to Mother.


WHICHWAY____________rate____________time______________distance
To Mother___________r_______________(___)_____________600
Back Home__________r-10_____________(___)_____________600


Fill in the time information, only as expressions.

WHICHWAY____________rate____________time______________distance
To Mother___________r_______________(600/r)_____________600
Back Home__________r-10_____________(600/(r-10))_____________600


Going back home took two hours longer.  
{{{highlight(600/r+2=600/(r-10))}}}
Stated another way, the time going to mother plus two more hours was the amount of time spent driving back home.  This is how that equation is formed.
Solve for r.
Begin by multiplying both sides of the equation by r(r+10) which will clear the denominators as you begin simplifying.


{{{600(r-10)+2r(r-10)=600r}}}
{{{600r-6000+2r^2-20=600r}}}
{{{-6000+2r^2-20=0}}}
{{{r^2=6020}}}
{{{highlight(r= 78)}}} mph