Question 1030704
Let {{{ s }}} = her speed in mi/hr going to the game
Let {{{ t }}} = her time in hrs going to the game
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equation going to the game
(1) {{{ 168 = s*t }}}
Equation for coming back from game
(2) {{{ 168 = ( s - 14 )*( t + 1 ) }}}
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(2) {{{ 168 = s*t - 14t + s - 14 }}}
(2) {{{ 168 = t*( s - 14 ) + s - 14 }}}
and
(1) {{{ t = 168/s }}}
Substitute (1) into (2)
(2) {{{ 168 = ( 168/s )*( s - 14 ) + s - 14 }}}
(2) {{{ 168 = 168 - 2352/s + s - 14 }}}
(2) {{{ s - 14 = 2352/s }}}
(2) {{{ s^2 - 14s = 2352 }}}
Complete the square
(2) {{{ s^2 - 14s + (14/2)^2 = 2352 + (14/2)^2 }}}
(2) {{{ s^2 - 14s + 49 = 2352 + 49 }}}
(2) {{{ ( s - 7 )^2 = 2401 }}}
(2) {{{ ( s - 7 )^2 = 49^2 }}}
Take the square root of both sides
(2) {{{ s - 7 = 49 }}}
(2) {{{ s = 56 }}}
She drove 56 mi/hr to the soccer game
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check:
(1) {{{ 168 = s*t }}}
(1) {{{ 168 = 56*t }}}
(1) {{{ t = 3 }}}
and
(2) {{{ 168 = ( s - 14 )*( t + 1 ) }}}
(2) {{{ 168 = ( 56 - 14 )*( 3 + 1 ) }}}
(2) {{{ 168 = 42*4 }}}
(2) {{{ 168 = 168 }}}
OK