Question 129394
Rate times time equals distance.
Your two equations are correct but watch the units.
It's 189 miles, not mph. 
1. {{{vt=189}}}
2. {{{(v+12)(t-1)=189}}} 
To solve you use one of the equations to get an expression for one of the variables in terms of the other and then substitute. 
From 1,
{{{vt=189}}}
{{{v=189/t}}}
Now substitute this value into 2,
{{{(v+12)(t-1)=189}}} 
{{{(189/t+12)(t-1)=189}}} 
Multiply both sides by t.
{{{t(189/t+12)(t-1)=189t}}} 
{{{(189+12t)(t-1)=189t}}} 
Use the FOIL method for the left hand side,
{{{(189)(t)+(189)(-1)+(12t)(t)+(12t)(-1)=189t}}}
{{{189t-189+12t^2-12t=189t}}}
{{{12t^2-12t-189=0}}}
{{{4t^2-4t-63=0}}}
You can factor this equation into,
{{{(2t-9)(2t+7)=0}}}
There are two solutions,
The first solution is,
{{{2t-9=0}}}
{{{t=9/2}}}
The second solution is,
{{{2t+7=0}}}
{{{t=-7/2}}}
For your equation, t represents time.
A negative time does not make sense in this application. 
You would use the positive answer for your solution.
{{{t=9/2}}}
Check your answer.
1. {{{vt=189}}}
{{{v(9/2)=189}}}
{{{v=42}}}
2. {{{(v+12)(t-1)=189}}} 
{{{(42+12)(9/2-1)=189}}}
{{{(9/2-2/2)=189/54}}}
{{{7/2=7/2}}}
Your answer leads to a true statement, it's a good answer.
The original average speed is 42 mph.