Question 662292
Let {{{ t }}} = his time spent jogging in hrs
{{{ 3 - t }}} = his time spent walking in hrs
Let {{{ w }}} = his speed walking in mi/hr
{{{ w + 4.5 }}} = his speed jogging
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Equation for jogging:
(1) {{{ 9 = ( w + 4.5 )*t }}}
Equation for walking:
(2) {{{ 9 = w*( 3 - t ) }}}
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(2) {{{ 9 = 3w - w*t }}}
(2) {{{ w*t = 3w - 9 }}}
(2) {{{ t = 3 - 9/w }}}
Substitute (2) into (1)
(1) {{{ 9 = ( w + 4.5 )*( 3 - 9/w )  }}}
(1) {{{ 9 = 3w + 13.5 - 9 - 40.5/w }}}
(1) {{{ 18 - 13.5 = 3w - 40.5/w }}}
(1) {{{ 4.5 = 3w - 40.5/w }}}
(1) {{{ 4.5w = 3w^2 - 40.5 }}}
(1) {{{ 3w^2 - 4.5w - 40.5 = 0 }}}
(1) {{{ 2w^2 - 3w - 27 = 0 }}}
use quadratic formula
{{{ w = (-(-3) +- sqrt( (-3)^2-4*2*(-27) ))  / (2*2) }}}
{{{ w = ( 3 +- sqrt( 9 + 216 ))  / 4 }}}
{{{ w = ( 3 +- sqrt( 225 ))  / 4 }}}
{{{ w = ( 3 + 15)  / 4 }}}
{{{ w = 18/4 }}}
{{{ w = 4.5 }}} ( ignore negative root )
{{{ w + 4.5 = 9 }}} 
he walks 4.5 mi/hr and jogs 9 mi/hr
check:
(2) {{{ 9 = 4.5*( 3 - t ) }}}
(2) {{{ 9 = 13.5 - 4.5t }}}
(2) {{{ 4.5t = 13.5 - 9 }}}
(2) {{{ 4.5t = 4.5 }}}
{{{ t = 1 }}}
and
(1) {{{ 9 = ( 4.5 + 4.5 )*t }}}
(1) {{{ 9 = 9t }}}
{{{ t = 1 }}}
OK