Question 1042731
Let {{{ s }}} = his jogging speed in mi/hr
{{{ s + 4 }}} = his biking speed in mi/hr
Let {{{ t }}} = his time spent jogging in hrs
{{{ 1 - t }}} = his time spent biking in hrs
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Mike's equation for jogging:
(1) {{{ 3 = s*t }}}
Mike's equation for biking:
(2) {{{ 5 = ( s+4 )*( 1 - t ) }}}
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(1) {{{ t = 3/s }}}
Substitute (1) into (2)
(2) {{{ 5 = ( s+4 )*( 1 - 3/s ) }}}
(2) {{{ 5 = s + 4 - 3 - 12/s }}}
(2) {{{ 4 = s - 12/s }}}
(2) {{{ 4s = s^2 - 12 }}}
(2) {{{ s^2 - 4s - 12 = 0 }}}
(2) {{{ ( s - 6 )*( s + 2 ) = 0 }}} ( by inspection )
{{{ s = 6 }}} ( speed has to be positive )
and
{{{ s + 4 = 10 }}}
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Mike's jogging speed is 6 mi/hr
Mike's biking speed is 10 mi/hr
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check:
(1) {{{ 3 = s*t }}}
(1) {{{ 3 = 6*t }}}
(1) {{{ t = 1/2 }}} hr
and
(2) {{{ 5 = ( s+4 )*( 1 - t ) }}}
(2) {{{ 5 = ( 6+4 )*( 1 - t ) }}}
(2) {{{ 5 = 10*( 1 - t ) }}}
(2) {{{ 5 = 10 - 10t }}}
(2) {{{ 10t = 5 }}}
(2) {{{ t = 1/2 }}} hr
OK