Question 1033338
Let {{{ d }}} = distance in miles 
traveled on 1st part of trip
Let {{{ t }}} = time in hrs for 1st
part of trip
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1st part of trip:
(1) {{{ d = 54t }}}
2nd part of trip:
(2) {{{ 318 - d = 61*( 5.5 - t ) }}}
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(2) {{{ 318 - d = 335.5 - 61t }}}
(2) {{{ d = 61t - 17.5 }}}
Substitute (1) into (2)
(2) {{{ 54t = 61t - 17.5 }}}
(2) {{{ 7t = 17.5 }}}
(2) {{{ t = 2.5 }}}
and
{{{ 5.5 - t = 5.5 - 2.5 }}}
{{{ 5.5 - t = 3 }}}
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He traveled for 2.5 hrs at 54 mi/hr
He traveled for 3 hrs at 61 mi/hr
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check:
(1) {{{ d = 54t }}}
(1) {{{ d = 54*2.5 }}}
(1) {{{ d = 135 }}} mi
and
(2) {{{ 318 - d = 61*( 5.5 - t ) }}}
(2) {{{ 318 - d = 61*( 5.5 - 2.5 ) }}}
(2) {{{ 318 - d = 61*3 }}}
(2) {{{ 318 - d = 183 }}}
(2) {{{ d = 318 - 183 }}}
(2) {{{ d = 135 }}} mi
OK