Question 1002933
Let {{{ s }}} = her speed in mi/hr on her way back home
{{{ s + 24 }}} = her speed going to parents in mi/hr
Let {{{ t }}} = her time in hrs going back home
{{{ 14 - t }}} = her time in hrs going to parents
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Equation for going to parents:
(1) {{{ 490 = ( s + 24 )*( 14 - t ) }}}
Equation for going back home:
(2) {{{ 490 = s*t }}}
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(1) {{{ 490 = 14s + 336 - s*t - 24t }}}
and, since 
(2) {{{ t = 490/s }}}
(1) {{{ 490 = 14s + 336 - 490 - 24*( 490/s ) }}}
(1) {{{ 490 + 154 = 14s - 11760/s }}}
Multiply both sides by {{{s}}}
(1) {{{ 644s = 14s^2 - 11760 }}}
(1) {{{ 14s^2 - 644s - 11760 = 0 }}}
(1) {{{ s^2 - 46s = 840 }}}
Complete the square
(1) {{{ s^2 - 46s + (46/2)^2 = 840 + (46/2)^2 }}}
(1) {{{ s^2 - 46s + 529 = 840 + 529 }}}
(1) {{{ ( s - 23 )^2 = 1369 }}}
Take the square root of both sides
(1) {{{ s - 23 = 37 }}}
(1) {{{ s = 60 }}}
and
{{{ s + 24 = 60 + 24 }}}
{{{ s + 24 = 84 }}}
Her speed on her way back home was 60 mi/hr
Her speed going to parents was 84 mi/hr
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check the answer
(2) {{{ t = 490/s }}}
(2) {{{ t = 490/60 }}}
(2) {{{ t = 8.1667 }}}
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(1) {{{ 490 = ( s + 24 )*( 14 - t ) }}}
(1) {{{ 490 = ( 60 + 24 )*( 14 - t ) }}}
(1) {{{ 490 = 84*( 14-t ) }}}
(1) {{{ 490 = 1176 - 84t }}}
(1) {{{ 84t = 1176 - 490 }}}
(1) {{{ 84t = 686 }}}
(1) {{{ t = 8.1667 }}}
OK