Question 558016
Let {{{ s }}} = her speed with no wind
Let {{{ w }}} = the wind speed
{{{ s + w }}} = biking speed with the wind
{{{ s - w }}} = biking speed against the wind
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given:
(1) {{{ 1 = ( s + w )*3 }}}
(2) {{{ 1 = ( s - w )*4 }}}
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(1) {{{ 1 = 3s + 3w }}}
(2) {{{ 1 = 4s - 4w }}}
Multiply both sides of (1) by {{{4}}}
and both sides of (2) by {{{3}}}
Then add the equations
(1) {{{ 4 = 12s + 12w }}}
(2) {{{ 3 = 12s - 12w }}}
{{{ 7 = 24s }}}
{{{ s = 7/24 }}} mi/min
{{{ 7/24 }}} mi/min x {{{ 60 }}} min/mi = {{{ 17.5 }}} mi/hr
and
(1) {{{ 1 = 3s + 3w }}}
(1) {{{ 1 = 3*(7/24) + 3w }}}
(1) {{{ 3w = 24/24 - 21/24 }}}
(1) {{{ 3w = 3/24 }}}
(1) {{{ w = 1/24 }}} mi/min
{{{ 1/24 }}} mi/min x {{{ 60 }}} min/hr = {{{ 2.5 }}} mi/hr
The wind speed was 2.5 mi/hr
check answer:
(1) {{{ 1 = ( s + w )*(3/60) }}} (note that {{{3}}} min = {{{ 3/60 }}} hrs)
(1) {{{ 1 = ( 17.5 + 2.5 )*(3/60) }}}
(1) {{{ 1 =  20*(3/60) }}}
(1) {{{ 1 = 60/60 }}}
(1) {{{ 1 = 1 }}}
and
(2) {{{ 1 = ( s - w )*(4/60) }}} 
(2) {{{ 1 = ( 17.5 - 2.5 )*(4/60) }}}
(2) {{{ 1 = 15*(4/60) }}}
(2) {{{ 1 = 60/60 }}}
(2) {{{ 1= 1 }}}
'OK