Question 934938
Let {{{ w }}} = the speed of the wind
Let {{{ s }}} = the speed of the plane in still air
{{{ s - w }}} = speed of the plane going against the wind
{{{ s + w }}} = speed of the plane going with the wind
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(1) {{{ 390 = ( s - w )*3 }}}
(2) {{{ 390 = ( s + w )*2.5 }}}
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(1) {{{ 390 = 3s - 3w }}}
(2) {{{ 390 = 2.5s + 2.5w }}}
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Multiply both sides of (1) by {{{ 5 }}}
(1) {{{ 1950 = 15s - 15w }}}
Multiply both sides of (2) by {{{ 6 }}}
(2) {{{ 2340 = 15s + 15w }}}
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Add the equations
{{{ 4290 = 30s }}}
{{{ s = 143 }}}
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By substitution:
(1) {{{ 390 = 3s - 3w }}}
(1) {{{ 130 = s - w }}}
(1) {{{ 130 = 143 - w }}}
(1) {{{ w = 13 }}}
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The speed of the wind is 13 mi/hr
The speed of the plane in still air is 143 mi/hr
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check:
(1) {{{ 390 = ( s - w )*3 }}}
(1) {{{ 390 = ( 143 - 13 )*3 }}}
(1) {{{ 390 = 130*3 }}}
(1) {{{ 390 = 390 }}}
You can check other equation