Question 648721
Let {{{ b }}} = bird's speed with no wind
Let {{{ w }}} = the speed of the wind
{{{ w/2 }}} = half of the wind speed
{{{ b - w }}} = bird's speed flying against the wind
{{{ b + w }}} = bird's speed flying with the wind
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given:
(1) {{{ 90 = b + w }}}
(2) {{{ 30 = b - w/2 }}}
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Multiply both sides of (2) by {{{2}}}
(2) {{{ 60 = 2b - w }}}
(2) {{{ 2b - w = 60 }}}
and
(1) {{{  b + w = 90 }}}
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add the equations
{{{ 3b = 150 }}}
{{{ b = 50 }}} 
and, since
(1) {{{  b + w = 90 }}}
(1) {{{ w = 90 - 50 }}}
(1) {{{ w = 40 }}}
The bird's speed with no wind is 50 km/hr
The speed of the wind is 40 km/hr
check:
(2) {{{ 30 = b - w/2 }}}
(2) {{{ 30 = 50 - 40/2 }}}
(2) {{{ 30 = 50 - 20 }}}
(2) {{{ 30 = 30 }}}
and
(1) {{{ 90 = b + w }}}
(1) {{{ 90 = 50 + 40 }}}
(1) {{{ 90 = 90 }}}
OK