Question 996403
{{{ 36/60 = .6 }}}
Let {{{ s }}} = the speed of the plane in still air in mi/hr
Let {{{ w }}} = the speed of the wind in mi/hr
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Equation for flying with the wind:
(1) {{{ 2800 = ( s + w )*5 }}}
Equation for flying against the wind:
(2) {{{ 2800 = ( s - w )*5.6 }}}
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(1) {{{ 2800 = 5s + 5w }}}
and
(2) {{{ 2800 = 5.6s - 5.6w }}}
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{{{ 5.6 = .8*7 }}}
(2) {{{ 2800 = .8*7*s - .8*7*w }}}
(2) {{{ 2800/.8 = 7s - 7w }}}
(2) {{{ 7s - 7w = 3500 }}}
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Multiply both sides of (1) by {{{ 7 }}}
and both sides of (2) by {{{ 5 }}}
then add the equations
(1) {{{ 35s + 35w = 19600 }}}
(2) {{{ 35s - 35w = 17500 }}}
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{{{ 70s = 37100 }}}
{{{ s = 530 }}}
and
(1) {{{ 5s + 5w = 2800 }}}
(1) {{{ 5*530 + 5w = 2800 }}}
(1) {{{ 2650 + 5w = 2800 }}}
(1) {{{ 5w = 150 }}}
(1) {{{ w = 30 }}}
the speed of the plane in still air is 530 mi/hr
the speed of the wind is 30 mi/hr
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To check, plug numbers back into equations