Question 1054727
Let {{{ s }}} = her speed driving back home in mi/hr
{{{ s + 25 }}} = her speed driving to parents in mi/hr
Let {{{ t }}} = her time in hrs to drive back home
{{{ 29 - t }}} = her time driving to parents house in hrs
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Driving to parents house:
(1) {{{ 870 = ( s+25 )*( 29 - t ) }}}
Driving back home:
(2) {{{ 870 = s*t }}}
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(2) {{{ t = 870/s }}}
Plug (2) into (1)
(1) {{{ 870 = ( s+25 )*( 29 - 870/s ) }}}
(1) {{{ 870 = 29s + 725 - 870 - 21750/s }}}
(1) {{{ 1740 - 725 = 29s - 21750/s }}}
(1) {{{ 1015 = 29s - 21750/s }}}
(1) {{{ 1015s = 29s^2 - 21750 }}}
(1) {{{ 29s^2 - 1015s - 21750 = 0 }}}
(1) {{{ s^2 - 35s - 750 = 0 }}}
(1) {{{ ( s - 50 )*( s + 15 ) = 0 }}} ( by looking at this )
{{{ s = 50 }}} ( because the speed must be positive )
and
{{{ s + 25 = 75 }}}
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Her speed driving back home in mi/hr is 50 mi/hr
Her speed driving to parents in mi/hr is 75 mi/hr
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check:
(2) {{{ 870 = s*t }}}
(2) {{{ 870 = 50t }}}
(2) {{{ t = 17.4 }}} hrs
and
(1) {{{ 870 = ( 50+25 )*( 29 - t ) }}}
(1) {{{ 870 = 75*( 29 - t ) }}}
(1) {{{ 870 = 2175 - 75t }}}
(1) {{{ 75t = 1305 }}}
(1) {{{ t = 17.4 }}} hrs
OK