Question 944976
Let {{{ t }}} = time spent on highway in hours
{{{ 6 - t }}} = time spent on back road in hours
Let {{{ d }}} = distance traveled on highway in miles
{{{ 370 - d }}} = distance traveled on back roads in miles
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On highway:
(1) {{{ d = 70t }}}
On back roads:
(2) {{{ 370 - d = 45*(  6 - t ) }}}
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(2) {{{ 370 - d = 270 - 45t }}}
Substitute (1) into (2)
(2) {{{ 370 - 70t = 270 - 45t }}}
(2) {{{ 100 = 25t }}}
(2) {{{ t = 4 }}}
{{{ 6 - t = 6 - 4 }}}
{{{ 6 - t = 2 }}}
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You spent 4 hrs on highway
You spent 2 hrs on back roads
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check:
(1) {{{ d = 70t }}}
(1) {{{ d = 70*4 }}}
(1) {{{ d = 280 }}}
and
(2) {{{ 370 - d = 45*(  6 - t ) }}}
(2) {{{ 370 - d = 45*2 }}}
(2) {{{ d = 370 - 90 }}}
(2) {{{ d = 280 }}}
OK