Question 334470
You can write 2 equations, 1 for driving to the house and
1 for returning. The distance is unknown, but it's the 
same for both trips. I'll call the distance {{{d}}}
I'll call the time to drive to the house {{{t}}}. Since the
total driving time is {{{12}}} hrs, the time to drive back
is {{{12 - t}}}
Driving to the house:
(1) {{{d = r[1]*t}}}
Drive from the house:
(2) {{{d = r[2]*(12 - t)}}}
given:
{{{r[1] = 55}}} mi/hr
{{{r[2] = 65}}} mi/hr
-------------------------
Now I can write:
(1) {{{d = 55t}}}
(2) {{{d = 65*(12 - t)}}}
I can set (1) and (2) equal to eachother:
{{{55t = 65*(12 - t)}}}
{{{55t = 780 - 65t}}}
{{{120t = 780}}}
{{{t = 6.5}}}
It took 6.5 hrs to drive to the house.
Now find {{{d}}}
{{{d = 55t}}}
{{{d = 55*6.5}}}
{{{d = 357.5}}} mi
You drove the same distance coming back, so
the total distance is {{{2d}}}
{{{2d = 2*357.5}}}
{{{2d = 715}}}
You drove 715 mi
check answer:
{{{2d = 55t + 65*(12 - t)}}}
{{{715 = 55*6.5 + 65*(12 - 6.5)}}}
{{{715 = 357.5 + 65*5.5}}}
{{{715 = 357.5 + 357.5}}}
{{{715 = 715}}}
OK