Question 887707
Let r = the certain speed going.

________________rate_______time________distance
NASHVILLE_______r
BACK FROM_______r+40
TOTAL_______________________8___________600


The question asks for r+40 but you want to solve for r first (the way the variables were here assigned).


RT=D for rate time distance, so T and D can be found accordingly.


________________rate_______time________distance
NASHVILLE_______r___________x__________rx
BACK FROM_______r+40_______8-x______(r+40)(8-x)
TOTAL_______________________8___________600

Not seeing any progress with that chart.


________________rate_______time________distance
NASHVILLE_______r__________x___________rx
BACK FROM_______r+40________y________(r+40)y
TOTAL_______________________8___________600
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This gives only two equations but three unknowns.
------------------------
{{{x+y=8}}}
{{{rx+ry+40y=600}}}
------------------------

The "600" equation is also {{{r(x+y)+40y=600}}}
{{{r*8+40y=600}}}
{{{r+5y=75}}}


This would seem to give a system:
----------
{{{highlight_green(x+y=8)}}}
-
{{{highlight_green(r+5y=75)}}}
----------


Which could have more than one solution.