Question 956727
Back at you -looks OK now
Let {{{ w }}} = the windspeed in mi/hr
Let {{{ s }}} = the speed of the plane in still air in mi/hr
{{{ s - w }}} = the speed of the plane flying into the wind in mi/hr
{{{ s + w }}} = the speed of the plane flying with the wind in mi/hr
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Flying into the wind:
(1) {{{ 780 = ( s - w )*2 }}}
Flying with the wind:
(2) {{{ 780 = ( s + w )*(3/2) }}}
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(1) {{{ 780 = 2s - 2w }}}
and
(2) {{{ 1560 = 3s + 3w }}}
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Multiply both sides of ( 1 ) by {{{ 3/2 }}}
and add the equations
(1) {{{ 1170 = 3s - 3w }}}
(2) {{{ 1560 = 3s + 3w }}}
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{{{ 2730 = 6s }}}
{{{ s = 455 }}}
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(1) {{{ 780 = 2*455 - 2w }}}
(1) {{{ 2w = 910 - 780 }}}
(1) {{{ 2w = 130 }}}
(1) {{{ w = 65 }}}
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The windspeed is 65 mi/hr
The speed of the plane in still air is 455 mi/hr
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check:
(2) {{{ 780 = ( s + w )*(3/2) }}}
(2) {{{ 780 = ( 455 + 65 )*(3/2) }}}
(2) {{{ 780 = 520*(3/2) }}}
(2) {{{ 1560 = 1560 }}}
OK
(1) {{{ 780 = ( s - w )*2 }}}
(1) {{{ 780 = ( 455 - 65 )*2 }}}
(1) {{{ 780 = 390*2 }}}
(1) {{{ 780 = 780 }}}
OK