Question 660269
Let {{{ t }}} = time spent driving at 15 mi/hr
{{{ 6 - t }}} = time spent driving at 55 mi/hr
Let {{{ d }}} = distance driven at 15 mi/hr
{{{ 300 - d }}} = distance driven at 55 mi/hr
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given:
(1) {{{ d = 15t }}}
(2) {{{ 300 - d = 55*( 6 - t ) }}}
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Substitute (1) into (2)
(2) {{{ 300 - 15t = 55*( 6 - t ) }}}
(2) {{{ 300 - 15t = 330 - 55t }}}
(2) {{{ 55t - 15t = 330 - 300 }}}
(2) {{{ 40t = 30 }}}
(2) {{{ t = 3/4 }}}
and
(1) {{{ d = 15t }}}
(1) {{{ d = 15*(3/4) }}}
(1) {{{ d = 45/4 }}}
(1) {{{ d = 11.25 }}}
She drove 11.25 mi at 15 mi/hr
check:
(2) {{{ 300 - d = 55*( 6 - t ) }}}
(2) {{{ 300 - 11.25 = 55*( 6 - t ) }}}
(2) {{{ 288.75 = 55*( 6 - t ) }}}
(2) {{{ 288.75 = 330 - 55t }}}
(2) {{{ 55t = 330 - 288.75 }}}
(2) {{{ 55t = 41.25 }}}
(2) {{{ t = .75 }}}
(2) {{{ t = 3/4 }}}
OK