Question 733167
rates:
biking: {{{ r }}} mi/hr
running: {{{ r - 4 }}} mi/hr
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distances:
biking: {{{ 20 }}} mi
running: {{{ 12 }}} mi
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times:
biking: {{{ 20/r }}} hrs
running: {{{ 12/( r - 4 ) }}}
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{{{ 20/r + 12/(r - 4) = 4 }}}
Multiply both sides by {{{ r*( r - 4 ) }}}
{{{ 20*( r - 4 ) + 12r = 4r*( r - 4 ) }}}
{{{ 20r - 80 + 12r = 4r^2 - 16r }}} 
{{{ 4r^2 - 20r - 16r - 12r + 80 = 0 }}}
{{{ 4r^2 - 48r + 80 = 0 }}}
{{{ r^2 - 12r + 20 = 0 }}}
{{{ ( r - 2 )*( r - 10 ) = 0 }}}
The 2 answers are:
{{{ r = 2 }}}
{{{ r = 10 }}}
{{{ r }}} can't be {{{ 2 }}} since I have to subtract {{{ 4 }}} from it
to get the running speed, so
Jen's rate while biking is 10 mi/hr
check:
{{{ 20*( r - 4 ) + 12r = 4r*( r - 4 ) }}}
{{{ 20*( 10 - 4 ) + 12*10 = 4*10*( 10 - 4 ) }}}
{{{ 20*6 + 120 = 40*6 }}}
{{{ 240 = 240 }}}
OK