Question 1045761
Let {{{ d }}} = the distance traveled by bus in km
{{{ 1900 - d }}} = the distance traveled by plane
Let {{{ t }}} = time in hrs spent traveling by bus
{{{ 5 - t }}} = time in hrs spent traveling by plane
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Equation for bus:
(1) {{{ d = 60t }}}
Equation for plane:
(2) {{{ 1900 - d = 700*( 5 - t ) }}}
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(1) {{{ t = d/60 }}}
Plug this result into (2)
(2) {{{ 1900 - d = 700*( 5 - d/60 ) }}}
(2) {{{ 1900 - d = 3500 - (35/3)*d }}}
(2) {{{ 5700 - 3d = 10500 - 35d }}}
(2) {{{ 32d = 4800 }}}
(2) {{{ d = 150 }}}
and
{{{ 1900 - d = 1900 - 150 }}}
{{{ 1900 - d = 1750 }}}
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She traveled 150 km by bus and 1750 km by plane
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check:
(1) {{{ t = d/60 }}}
(1) {{{ t = 150/60 }}}
(1) {{{ t = 2.5 }}} hrs by bus
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(2) {{{ 1900 - d = 700*( 5 - t ) }}}
(2) {{{ 1900 - 150 = 700*( 5 - t ) }}}
(2) {{{ 1750 = 700*( 5 - t ) }}}
(2) {{{ 5 - t - 2.5 }}} by plane
{{{ 2.5 + 2.5 = 5 }}} hrs total
OK