Question 563293
Let {{{ s }}} = speed of the car
Let {{{ t }}} = time for trip
given:
(1) {{{ 624 = s*t }}}
(2) {{{ 624 = ( s + 4 )*( t - 1 ) }}}
-----------------------
(2) {{{ 624 = s*t + 4t - s - 4 }}}
and
(1) {{{ t = 624/s }}}
Substitute this into (2) 
(2) {{{ 624 = s*( 624/s ) + 4*( 624/s ) - s - 4 }}}
(2) {{{ 624 = 624 + 2496/s - s - 4 }}}
(2) {{{ 2496/s = s + 4 }}}
(2) {{{ 2496 = s^2 + 4s }}}
(2) {{{ s^2 + 4s - 2496 = 0 }}}
Use quadratic formula
{{{ s = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 
{{{ a = 1 }}}
{{{ b = 4 }}}
{{{ c = -2496 }}}
{{{ s = (-4 +- sqrt( 4^2 - 4*1*(-2496) )) / (2*1) }}} 
{{{ s = (-4 +- sqrt( 16 + 9984 )) / 2 }}} 
{{{ s = (-4 +- sqrt( 10000 )) / 2 }}} 
{{{ s = (-4 + 100) / 2 }}} 
{{{ s = 96/2 }}}
{{{ s = 48 }}} ( I can ignore the (-) square root )
Her average speed is 48 mi/hr
check answer:
(1) {{{ 624 = s*t }}}
(1) {{{ 624 = 48t }}}
(1) {{{ t = 13 }}}
and
(2) {{{ 624 = ( 48 + 4 )*( 13 - 1 ) }}}
(2) {{{ 624 = 52*12 }}}
(2) {{{ 624 = 624 }}}
OK