Question 1148226
Let {{{ t }}} = time in hrs for the jet
{{{ 8 - t }}} = time in hrs for the prop plane
Let {{{ s }}} = the speed of the prop plane in mi/hr
{{{ 4s }}} = the speed in mi/hr of the jet
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Equation for jet:
(1) {{{ 1800 = 4s*t }}}
(1) {{{ 450 = s*t }}}
Equation for prop plane:
(2) {{{ 200 = s*( 8 - t ) }}}
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(1) {{{ s = 450/t }}}
Plug (1) into (2)
(2) {{{ 200 = ( 450/t )*( 8 - t ) }}}
(2) {{{ 200t = 3600 - 450t }}}
(2) {{{ 650t = 3600 }}}
(2) {{{ t = 72/13 }}}
and
(1) {{{ 450 = s*t }}}
(1) {{{ 450 = s*(72/13) }}}
(1) {{{ s = 450*(13/72) }}}
(1) {{{ s = 4850/72 }}}
(1) {{{ s = 81.25 }}}
and
{{{ 4s = 325 }}}
The speed of the jet is 325 mi/hr
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check answer:
(1) {{{ 1800 = 4s*t }}}
(1) {{{ 1800 = 325*(72/13) }}}
(1) {{{ 1800 = 1800 }}}
OK
(2) {{{ 200 = s*( 8 - t ) }}}
(2) {{{ 200 = 81.25*( 8 - 72/13 ) }}}
(2) {{{ 200 = 650 - 450 }}}
(2) {{{ 200 = 200 }}}
OK
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