Question 690247
Let {{{ d }}} = the distance traveled at {{{ 65 }}} mi/hr
{{{ 189 - d }}} = the distance traveled at {{{ 55 }}} mi/hr
Let {{{ t }}} = his time spent traveling at {{{ 65 }}} mi/hr
{{{ 3- t }}} = his time spent traveling at {{{ 55 }}} mi/hr
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Equation for {{{ 65 }}} mi/hr:
(1) {{{ d = 65t }}}
Equation for {{{ 55 }}} mi/hr:
(2) {{{ 189 - d = 55*( 3 - t ) }}}
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(2) {{{ 189 - d = 165 - 55t }}}
Substitute (1) into (2) 
(2) {{{ 189 - 65t = 165 - 55t }}}
(2) {{{ 65t - 55t = 189 - 165 }}}
(2) {{{ 10t = 24 }}}
(2) {{{ t = 2.4 }}}
{{{ .4*60 = 24 }}} 
{{{ 3 - 2.4 = .6 }}}
{{{ .6*60 = 36 }}}
He spent 2 hrs and 24 min traveling at {{{ 65 }}} mi/hr
He spent 36 min traveling at {{{ 55 }}} mi/hr
check answer:
(2) {{{ 189 - d = 55*( 3 - t ) }}}
(2) {{{ 189 - d = 55*( 3 - 2.4 ) }}}
(2) {{{ 189 - d = .6*55 }}}
(2) {{{ d = 189 - 33 }}}
(2) {{{ d = 156 }}}
and
(1) {{{ d = 65t }}}
(1) {{{ d = 65*2.4 }}}
(1) {{{ d = 156 }}}
OK