Question 1054145
Let {{{ d }}} = distance in miles traveled
on the 1st part of the trip
{{{ 339.5 - d }}} = distance in miles traveled 
on the 2nd part of the trip
Let {{{ t }}} = time in hrs for 1st part of the trip
{{{ 6 - t }}} = time in hrs for the 2nd part of the trip
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Equation for the 1st part:
(1) {{{ d = 56t }}}
Equation for the 2nd part:
(2) {{{ 339.5 - d = 57*( 6 - t ) }}}
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(2) {{{ 339.5 - d = 342 - 57t }}}
Plug (1) into (2)
(2) {{{ 339.5 - 56t = 342 - 57t }}}
(2) {{{ 57t - 56t = 342 - 339.5 }}}
(2) {{{ t = 2.5 }}}
and
{{{ 6 - t = 6 - 2.5 }}}
{{{ 6 - t = 3.5 }}}
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He traveled for 2.5 hrs at 56 mi/hr
He traveled for 3.5 hrs at 57 mi/hr
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check:
(1) {{{ d = 56t }}}
(1) {{{ d = 56*2.5 }}}
(1) {{{ d = 140 }}} mi
and
(2) {{{ 339.5 - d = 57*( 6 - 2.5 ) }}}
(2) {{{ 339.5 - d = 342 - 142.5 }}}
(2) {{{ d = 339.5 - 342 + 142.5 }}}
(2) {{{ d = 482 - 342 }}}
(2) {{{ d = 140 }}} mi
OK