Question 1057791
Let {{{ s }}} = her average speed going back home
{{{ s + 5 }}} = her average speed going to friend's house
Let {{{ t }}} = her time in hrs going back home
{{{ 2 - t }}} = her time in hrs going to friend's house
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Equation for going to friend's house:
(1) {{{ 12 = ( s + 5 )*( 2 - t ) }}}
Equation for going back home:
(2) {{{ 12 = s*t }}}
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(2) {{{ t = 12/s }}}
Plug this result back into (1)
(1) {{{ 12 = ( s + 5 )*( 2 - 12/s ) }}}
(1) {{{ 12 = 2s + 10 - 12 - 60/s }}}
(1) {{{ 14 = 2s - 60/s }}}
(1) {{{ 14s = 2s^2 - 60 }}}
(1) {{{ 2s^2 - 14s - 60 = 0 }}}
(1) {{{ s^2 - 7s - 30 = 0 }}}
(1) {{{ ( s - 10 )*( s + 3 ) = 0 }}} ( by looking at it )
(1) {{{ s = 10 }}} ( can't use the negative solution )
and
{{{ s + 5 = 15 }}}
Going to friend's house: 15 mi/hr
Going back home: 10 mi/hr
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check:
(2) {{{ 12 = s*t }}}
(2) {{{ 12 = 10t }}}
(2) {{{ t = 1.2 }}} hrs
and
(1) {{{ 12 = ( s + 5 )*( 2 - t ) }}}
(1) {{{ 12 = 15*( 2 - t ) }}}
(1) {{{ 12 = 30 - 15t }}}
(1) {{{ 15t = 30 - 12 }}}
(1) {{{ 15t = 18 }}}
(1) {{{ t = 1.2 }}} hrs
OK