Question 1098657
Let {{{ s }}} = the speed of the plane in still air
Let {{{ w }}} = the wind speed
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Flying against the wind:
(1) {{{ 360 = ( s - w )*3 }}}
Flying with the wind:
(2) {{{ 360 = ( s + w )*2.5 }}}
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(1) {{{ 3s - 3w = 360 }}}
(2) {{{ 2.5s + 2.5w = 360 }}}
Multiply both sides of (1) by {{{ 5 }}}
and both sides of (2) by {{{ 6 }}}
Then add the equations
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(1) {{{ 15s - 15w = 1800 }}}
(2) {{{ 15s + 15w = 2160 }}}
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{{{ 30s = 3960 }}}
{{{ s = 132 }}}
and
(1) {{{ 360 = ( s - w )*3 }}}
(1) {{{ 360 = ( 132 - w )*3 }}}
(1) {{{ 360 = 396 - 3w }}}
(1) {{{ 3w = 36 }}}
(1) {{{ w = 12 }}}
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The speed of the plane in still air is 132 mi/hr
The wind speed is 12 mi/hr
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check:
(2) {{{ 360 = ( s + w )*2.5 }}}
(2) {{{ 360 = ( 132 + 12 )*2.5 }}}
(2) {{{ 360 = 144*2.5 }}}
(2) {{{ 360 = 360 }}}
OK