Question 1006534
Let {{{ p }}} = the average speed of the
plane in still air
{{{ p + 27 }}} = the average speed of the
plane flying with the wind
{{{ p - 27 }}} = the average speed of the
plane flying against the wind
Let {{{ t }}} = time in hrs
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Equation for flying with the wind:
(1) {{{ 490 = ( p + 27 )*t }}}
Equation for flying against the wind:
(2) {{{ 310 = ( p - 27 )*t }}}
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(1) {{{ t = 490 / ( p + 27 ) }}}
Substitute this result into (2)
(2) {{{ 310 = ( p - 27 )*( 490 / ( p + 27 ) ) }}}
Multiply both sides by {{{ p + 27 }}}
(2) {{{ 310*( p + 27 ) = 490*( p - 27 ) }}}
(2) {{{ 310p + 8370 = 490p - 13230 }}}
(2) {{{ 180p = 21600 }}}
(2) {{{ p = 120 }}}
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The plane's speed in still air is 120 mi/hr
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check:
(1) {{{ 490 = ( p + 27 )*t }}}
(1) {{{ 490 = ( 120 + 27 )*t }}}
(1) {{{ 490 = 147t }}}
(1) {{{ t = 3.333 }}} hrs ( 1 hr 20 min )
and
(2) {{{ 310 = ( p - 27 )*t }}}
(2) {{{ 310 = ( 120 - 27 )*t }}}
(2) {{{ 310 = 93t }}}
(2) {{{ t = 3.333 }}} hrs
OK