Question 836360
certain speed, r.

The trip is the same in both conditions, meaning the distance is the same.


{{{r*t=432}}}, the car traveled.


{{{(r+6)(t-1)=432}}}, if the speed higher as specified.


The question asks in effect, to find r.
TWO EQUATIONS IN TWO UNKNOWNS.


Notice what happens when multiplying for the "if" equation:
{{{rt+6t-r-6=432}}}
You already have an equation giving that rt=432, so simplify to 
{{{0+6t-r-6=0}}}
{{{highlight_green(6t-r-6=0)}}}.
USE the simpler, "car traveled" equation again, this time, solved for t.
{{{t=432/r}}};
Substitute this into the simplified "if" equation and solve for r.


{{{6(432/r)-r-6=0}}}
{{{6*432-r^2-6r=0}}}
{{{highlight_green(r^2+6r-6*432=0)}}}
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This equation is now  FOR YOU TO FINISH SOLVING.  There may be too many factorizations for the {{{6*432}}} for the purpose of trying to factor the quadratic member, so a better choice is to just form and compute the discriminant, and then use it in forming the solution or solutions for r.