Question 1085265
Let {{{ d }}} = the distance from home to school in km
Let {{{ s }}} = her speed in km/hr
Let {{{ t }}} =her time in hrs to go from home to school
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{{{ d = s*t }}}
Convert minutes to hrs
[ min ] x [ hrs/min ] = [ hrs ]
{{{ 15*( 1/60 ) = 1/4 }}} hrs
and, also:
{{{ 5*(1/60) = 1/12 }}} hrs
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Her equation for  a normal trip is:
(1) {{{ d = s*(1/4) }}}
If she increases her speed, the equation is:
(2) {{{ d = ( s + 5 )*( 1/4 - 1/12 ) }}}
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(2) {{{ d = ( s + 5 )*( 2/12 ) }}}
(2) {{{ d = ( s + 5 )*(1/6) }}}
Plug (1) into (2)
(2) {{{ (1/4)*s = ( s + 5 )*(1/6 ) }}}
Multiply both sides by {{{ 12 }}}
(2) {{{ 3s = 2*( s + 5 ) }}}
(2) {{{ 3s = 2s + 10 }}
(2) {{{ s = 10 }}} km/hr
and
(1) {{{ d = s*(1/4) }}}
(1) {{{ d = 10*(1/4) }}}
(1) {{{ d = 2.5 }}} km
The distance from home to school is 2.5 km
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check answer:
(2) {{{ d = ( s + 5 )*(1/6) }}}
(2) {{{ d = ( 10 + 5 )*(1/6) }}}
(2) {{{ d = 15/6 }}}
(2) {{{ d = 5/2 }}}
(2) {{{ d = 2.5 }}} km
OK