Question 1031959
Let {{{ s }}} = Doreen's speed in mi/hr
{{{ s + 10 }}} = Sue's speed in mi/hr
Let {{{ t }}} = Doreen's time in hrs to travel 50 mi
riding bicycle
{{{ t - 2 }}} = Sue's time in hrs to travel 60 mi
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Equation for Doreen:
(1) {{{ 50 = s*t }}}
Equation for Sue:
(2) {{{ 60 = ( s+10 )*( t - 2 ) }}}
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(1) {{{ s = 50/t }}}
Plug this into (2)
(2) {{{ 60 = ( 50/t +10 )*( t - 2 ) }}}
(2) {{{ 60 = 50 + 10t - 100/t - 20 }}}
(2) {{{ 30 = 10t - 100/t }}}
(2) {{{ 30t = 10t^2 - 100 }}}
(2) {{{ 10t^2 - 30t - 100 = 0 }}}
(2) {{{ t^2 - 3t - 10 = 0 }}}
(2) {{{ ( t - 5 )*( t + 2 ) = 0 }}} ( by looking at it )
{{{ t = 5 }}} ( time must be positive )
and
{{{ t - 2 = 3 }}}
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(1) {{{ 50 = s*5 }}}
(1) {{{ s = 50/5 }}}
(1) {{{ s = 10 }}} 
and
{{{ s+ 10 = 20 }}}
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Doreen's speed = 10 mi/hr
Doreen's time = 5 hrs
Sue's speed = 20 mi/hr
Sue's time = 3 hrs
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check answers:
(1) {{{ 50 = s*t }}}
(1) {{{ 50 = 10*5 }}}
(1) {{{ 50 = 50 }}}
and
(2) {{{ 60 = ( s+10 )*( t - 2 ) }}}
(2) {{{ 60 = 20*3 }}}
(2) {{{ 60 = 60 }}}
OK