Question 1084487
Let {{{ t }}} = time in hrs the plane flew at {{{ 600 }}} mi/hr
{{{ 5 - t }}} = time in hrs the plane flew at {{{ 550 }}} mi/hr
Let {{{ d }}} = distance in miles the plane flew at {{{ 600 }}} mi/hr
{{{ 2900 - d }}} = distance in miles the plane flew at {{{ 550 }}} mi/hr
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Flying with a tailwind:
(1) {{{ d = 600t }}}
Flying with a headwind:
(2) {{{ 2900 - d = 550*( 5 - t ) }}}
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Plug (1) into (2)
(2) {{{ 2900 - 600t = 550*( 5 - t ) }}}
(2) {{{ 2900 - 600t = 2750 - 550t }}}
(2) {{{ 50t = 150 }}}
(2) {{{ t = 3 }}}
and
{{{ 5 - t = 5 - 3 }}}
{{{ 5 - t = 2 }}}
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The plane flew for 3 hrs at 600 mi/hr
The plane flew for 2 hrs at 550 mi/hr
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check:
(1) {{{ d = 600t }}}
(1) {{{ d = 600*3 }}}
(1) {{{ d = 1800 }}} mi
and
(2) {{{ 2900 - d = 550*( 5 - t ) }}}
(2) {{{ 2900 - d = 550*2 }}}
(2) {{{ d = 2900 - 1100 }}}
(2) {{{ d = 1800 }}} mi
OK