Question 1035988
Let {{{ s }}} mi/hr = the plane's speed in still air
{{{ 20 }}} mi/hr = constant wind speed
Let {{{ t }}} = time in hrs traveling both
with the wind and against the wind
--------------------------------------
Equation for traveling against the wind:
(1) {{{ 430 = ( s - 20 )*t }}}
Equation for traveling with the wind:
(2) {{{ 470 = ( s + 20 )*t }}}
---------------------------
(1) {{{ t = 430 / ( s - 20 ) }}}
Plug this into (2)
(2) {{{ 470 = ( s + 20 )*( 430 / ( s - 20 ) ) }}}
(2) {{{ 470*( s - 20 ) = 430*( s + 20 ) }}}
(2) {{{ 470s - 9400 = 430s + 8600 }}}
(2) {{{ 40s = 18000 }}}
(2) {{{ s = 450 }}}
---------------
The speed of the plane in still air is 450 mi/hr
---------------
check:
(1) {{{ 430 = ( s - 20 )*t }}}
(1) {{{ 430 = ( 450 - 20 )*t }}}
(1) {{{ 430 = 430t }}}
(1) {{{ t = 1 }}} hr
and
(2) {{{ 470 = ( s + 20 )*t }}}
(2) {{{ 470 = ( 450 + 20 )*t }}}
(2) {{{ 470 = 470t }}}
(2) {{{ t = 1 }}} hr
OK
Sorry I did the whole thing -can't resist