Question 1071216
Let {{{ s }}} = her speed skateboarding to uncle's house
{{{ 2s }}} = her speed biking home
Let {{{ t }}} = time in hrs to skateboard to uncle's house
{{{ t - 2 }}} = time in hrs to return home by bike
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Equation for skateboarding:
(1) {{{ 12 = s*t }}}
Equation for biking:
(2) {{{ 12 = 2s*( t - 2 ) }}}
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(1) {{{ s = 12/t }}}
Plug this result into (2)
(2) {{{ 12 = 2*( 12/t )*( t - 2 ) }}}
(2) {{{ 6 = 12 - 24/t }}}
(2) {{{ 6 = 24/t }}}
(2) {{{ 6t = 24 }}}
(2) {{{ t = 4 }}} hrs
and
(1) {{{ 12 = s*4 }}}
(1) {{{ s = 3 }}} mi/hr
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{{{ t - 2 = 4 - 2 }}}
{{{ t - 2 = 2 }}}
It took her 2 hrs to get home by bike
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check:
(2) {{{ 12 = 2s*( t - 2 ) }}}
(2) {{{ 12 = 2*3*( 4 - 2 ) }}}
(2) {{{ 12 = 6*2 }}}
(2) {{{ 12 = 12 }}}
OK