Question 316082
The average speed is (total distance)/(total time)
Let {{{s}}} = her average speed speed
Let {{{t}}} = the time for the trip
given:
{{{576 = s*t}}}
{{{576 = (s + 8)*(t - 1)}}}
{{{576 = s*t + 8t - s - 8}}}
By substitution:
{{{576 = 576 + 8t - s - 8}}}
{{{0 = 8t - s - 8}}}
{{{s = 8t - 8}}}
Substituting again:
{{{576 = 8*(t - 1)*t}}}
{{{72 = (t - 1)*t}}}
{{{t^2 - t - 72 = 0}}}
Using quadratic formula:
{{{t = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{t = (-(-1) +- sqrt( (-1)^2-4*1*(-72) ))/(2*1) }}} 
{{{t = ( 1 +- sqrt( 1 + 288 )) / 2 }}}
{{{t = (1 + 17)/2}}} (ignore the negative root)
{{{t = 9}}}
And, since
{{{576 = s*t}}}
{{{576 = 9s}}}
{{{s = 64}}}
Her average speed for the trip is 64 mi/hr