Question 979823
Let {{{ s }}} = Jairus's speed in km/hr
{{{ s + 1 }}} = Arione's speed in km/hr
Let {{{ t + 1 }}} = Jairus's time in hrs
{{{ t }}} = Arione's time in hrs
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Jairus's equation:
(1) {{{ 90 = s*( t+1 ) }}}
Arione's equation:
(2) {{{ 90 = ( s+1 )*t }}}
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(2) {{{ s*t + t = 90 }}}
and
(1) {{{ s = 90/( t + 1 ) }}}
Substitute (1) into (2)
(2) {{{ ( 90/( t+1 ) )*t + t = 90 }}}
Multiply both sides by {{{ t+1 }}}
(2) {{{ 90t + t*( t+1 ) = 90*( t+1 ) }}}
(2) {{{ 90t + t^2 + t = 90t + 90 }}}
(2) {{{ t^2 + t - 90 = 0 }}}
I notice that {{{ 90 = 9*10 }}}, so
(2) {{{ ( t + 10 )*( t - 9 ) = 0 }}}
{{{ t = 9 }}} ( time must be positive )
and
(1) {{{ 90 = s*( t+1 ) }}}
(1) {{{ 90 = s*( 9+1 ) }}}
(1) {{{ 90 = 10s }}}
(1) {{{ s = 9 }}}
and
{{{ s+1 = 10 }}}
Ariones's rate is 10 km/hr
Jairus's rate is 9 km/hr
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check:
(2) {{{ 90 = ( s+1 )*t }}}
(2) {{{ 90 = ( 9+1 )*9 }}}
(2) {{{ 90 = 90 }}}
and
(1) {{{ 90 = s*( t+1 ) }}}
(1) {{{ 90 = 9*( 9+1 ) }}}
(1) {{{ 90 = 90 }}}
OK