Question 963224
Uniform Rates, Travel,  VT=D for rate time distance relationship.


____________________speed____________time__________distance
GOING________________r_______________(___)__________d
BACK_________________R______________(____)__________d
Total________________________________t


The data table has variables assigned as r=6, R=12, t=9, and d is unknown.


The rule VT=D gives T=D/V;
The general rule is using V as rate instead of R, because I already assigned R a specific value according to your problem's description.


____________________speed____________time__________distance
GOING________________r_______________d/r__________d
BACK_________________R______________d/R__________d
Total________________________________t


You have an obvious time sum equation:
{{{highlight_green(d/r+d/R=t)}}}.
Solve this equation for d.  Lowest common denominator is {{{r*R}}}.


{{{(d/r+d/R)*r*R=t*r*R}}}
{{{dR+dr=trR}}}
{{{d(R+r)=trR}}}
{{{highlight(d=(trR)/(r+R))}}}


Substitute the given values for t, r, and R and evaluate d.


You can go back now and evaluate the two time terms, {{{d/R}}} and {{{d/r}}}.