Question 743918
Let {{{ p }}} = the speed of the plane in still air in mi/hr
Let {{{ w }}} = the speed of the wind in mi/hr
{{{ p + w }}} = plane's speed flying with the wind in mi/hr
{{{ p - w }}} = plane's speed flying against the wind in mi/hr
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Flying with the wind:
(1) {{{ 510 = ( p + w )*3 }}}
Flying against the wind:
(2) {{{ 510 = ( p - w )*5 }}}
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(1) {{{ 3p + 3w = 510 }}}
and
(2) {{{ 5p - 5w = 510 }}}
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(1) {{{ p + w = 170 }}}
(2) {{{ p - w = 102 }}}
Add the equations
{{{ 2p = 272 }}}
{{{ p = 136 }}}
and
(1) {{{ 136 + w = 170 }}}
(1) {{{ w = 34 }}}
The rate of the plane in calm air is 136 mi/hr
The rate of the wind is 34 mi/hr
check:
(2) {{{ 136 - 34 = 102 }}}
(2) {{{ 102 = 102 }}}
OK