Question 890866
Let {{{ s }}} = the speed in mi/hr that would
get her there non time
Let {{{ t }}} = time in hrs spent driving to 
get her there on time
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(1) {{{ 100 = s*t }}}
(2) {{{ 100 = ( s + 8 )*((5/6)*t ) }}}
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(2) {{{ 600 = ( s + 8 )*5t }}}
and
(1) {{{ t = 100/s }}}
Substitute (1) into (2)
(2) {{{ 600 = ( s + 8 )*5*( 100/s ) }}}
(2) {{{ 600s = 500*( s + 8 ) }}}
(2) {{{ 600s = 500s + 4000 }}}
(2) {{{ 100s = 4000 }}}
(2) {{{ s = 40 }}}
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(1) {{{ t = 100/s }}}
(1) {{{ t = 100/40 }}}
(1) {{{ t = 5/2 }}} hrs
The trip actually took {{{ 60 * (5/2) = 150 }}} minutes
check:
(2) {{{ 100 = ( s + 8 )*((5/6)*t )
(2) {{{ 100 = ( 40 + 8 )*((5/6)*(5/2) )
(2) {{{ 100 = 48*( 25/12 ) }}}
(2) {{{ 100 = 25*4 }}}
(2) {{{ 100 = 100 }}}
OK