Question 1067639
Let {{{ t }}} = time in hrs spent on the train
{{{ 3 - t }}} = time in hrs spent on the bus
Let {{{ d }}} = distance in miles traveled by train
{{{ 167 - d }}} = distance in miles traveled by bus
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For the trip by train:
(1) {{{ d = 60t }}}
For the trip by bus:
(2) {{{ 167 - d = 50*( 3 - t ) }}}
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Substitute (1) into (2)
(2) {{{ 167 - 60t = 150 - 50t }}}
(2) {{{ 10t = 17 }}}
(2) {{{ t = 1.7 }}}
and
{{{ 3 - t = 3 - .7 }}}
{{{ 3 - t = 2.3 }}}
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He was on the train for 1.7 hrs
Also note: {{{ .7*60 = 42 }}} min
He was on the train for 1 hr 42 min
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check:
(1) {{{ d = 60t }}}
(1) {{{ d = 60*1.7 }}}
(1) {{{ d = 102 }}} miles
and
(2) {{{ 167 - d = 50*( 3 - t ) }}}
(2) {{{ 167 - d = 50*( 3 - 1.7 ) }}}
(2) {{{ 167 - d = 50*1.3 }}}
(2) {{{ 167 - d = 65 }}}
and
{{{ 102 + 65 = 167 }}} miles total