Question 942715
Let {{{ t }}} = time spent driving in hrs
{{{ 3.5 - t }}} = time spent walking in hrs
Let {{{ r }}} = his rate walking in mi/hr
{{{ 12r }}} = his rate driving in mi/hr
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Equation for driving:
(1) {{{ 72 = 12r*t }}}
Equation for walking:
(2) {{{ 4 = r*( 3.5 - t ) }}}
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(1) {{{ r = 6/t }}}
Substitute (1) into (2)
(2) {{{ 4 = ( 6/t )*( 3.5 - t ) }}}
(2) {{{ 4 = 21/t - 6 }}}
(2) {{{ 4t = 21 - 6t }}}
(2) {{{ 10t = 21 }}}
(2) {{{ t = 2.1 }}}
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(1) {{{ 72 = 12r*2.1 }}}
(1) {{{ 72 = 25.2r }}}
(1) {{{ r = 2.857 }}} mi/hr
The motorist walks at 2.857 mi/hr
check:
(2) {{{ 4 = r*( 3.5 - t ) }}}
(2) {{{ 4 = 2.857*( 3.5 - 2.1 ) }}}
(2) {{{ 4 = 2.857*1.4 }}}
(2) {{{ 4 = 4 }}}
OK