Question 644508
Let speed of plane in still air = {{{ p }}}
Let the wind speed  = {{{ w }}}
given:
Equation with the wind
(1) {{{ 400 = ( p + w )*4 }}}
Equation against the wind
(2) {{{ 400 = ( p - w )*8 }}}
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Multiply both sides of (1) 
by {{{ 2 }}} and
Add the equations
(1) {{{ 800 = 8p + 8w }}}
(2) {{{ 400 = 8p - 8w }}}
{{{ 1200 = 16p }}}
{{{ p = 75 }}}
Plug this result back into (1) or (2)
(1) {{{ 400 = ( 75 + w )*4 }}}
(1) {{{ 400 = 300 + 4w }}}
(1) {{{ 4w = 100 }}}
(1) {{{ w = 25 }}}
The speed of the plane in still air is 75 mi/hr
The wind speed is 25 mi/hr
check:
(2) {{{ 400 = ( 75 - 25 )*8 }}}
(2) {{{ 400 = 50*8 }}}
(2) {{{ 400 = 400 }}}
OK