Question 1112308
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) {{{ 720 = ( s + w )*3 }}}
Equation for flying against the wind:
(2) {{{ 720 = ( s - w )*4 }}}
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(1) {{{ 3s + 3w = 720 }}}
Multiply both sides by {{{ 4 }}}
(1) {{{ 12s + 12w = 2880 }}}
and
(2) {{{ 4s - 4w = 720 }}}
Multiply both sides by {{{ 3 }}}
(2) {{{ 12s - 12w = 2160 }}}
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Add (1) and (2)
(1) {{{ 12s + 12w = 2880 }}}
(2) {{{ 12s - 12w = 2160 }}}
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{{{ 24s = 5040 }}}
{{{ s = 210 }}}
and
(1) {{{ 3s + 3w = 720 }}}
(1) {{{ 3*210 + 3w = 720 }}}
(1) {{{ 630 + 3w = 720 }}}
(1) {{{ 3w = 90 }}}
(1) {{{ w = 30 }}}
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The wind speed is 30 mi/hr
The speed of the plane in still air is 210 mi/hr
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check answer:
(1) {{{ 720 = ( s+w )*3 }}}
(1) {{{ 720 = ( 210 + 30 )*3 }}}
(1) {{{ 720 = 240*3 }}}
(1) {{{ 720 = 720 }}}
and
(2) {{{ 720 = ( s-w )*4 }}}
(2) {{{ 720 = ( 210 - 30 )*4 }}}
(2) {{{ 720 = 180*4 }}}
(2) {{{ 720 = 720 }}}
OK