Question 496854
Let {{{w}}} = the wind speed
Let {{{p}}} = the speed of the plane in still air
Against the wind, the plane's speed is {{{ p - w }}}
With the wind, the plane's speed is {{{ p + w }}}
given:
Equation against the wind:
(1) {{{ 5005 = ( p - w )*7 }}}
With the wind:
(2) {{{ 5635 = ( p + w )*7 }}}
This is 2 equations and 2 unknowns, so it's solvable
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Add the equations
(1) {{{ 7p - 7w = 5005 }}}
(2) {{{ 7p + 7w = 5635 }}}
{{{ 14p = 10640 }}}
{{{ p = 760 }}}
and, since
(1) {{{ 7p - 7w = 5005 }}}
(1) {{{ 7*760 - 7w = 5005 }}}
(1) {{{ 5320 - 7w = 5005 }}}
(1) {{{ 7w = 5320 - 5005 }}}
(1) {{{ 7w = 315 }}}
(1) {{{ w = 45 }}}
The plane's speed in still air is 760 km/hr
The wind speed is 45 km/hr