Question 640952
Let {{{ t }}} = the time in hours he spent walking
{{{ 6 - t }}} = time in hours he spent on bike
Let {{{ d }}} = distance Jim walked in miles
{{{ 96 - d }}} = distance in miles he biked
Equation for walking:
(1) {{{ d = 4t }}}
Equation for biking:
(2) {{{ 96 - d = 20*( 6-t ) }}}
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Substitute (1) into (2)
(2) {{{ 96 - 4t = 120 - 20t }}}
(2) {{{ 20t - 4t = 120 - 96 }}}
(2) {{{ 16t = 24 }}}
(2) {{{ t = 3/2 }}}
{{{ 6 - t = 6 - 3/2 }}}
{{{ 6 - t = 9/2 }}}
Jim's time spent on bike is 4 and a half hours
check:
(1) {{{ d = 4*(3/2) }}}
(1) {{{ d = 6 }}}
and
(2) {{{ 96 - d = 20*( 6-(3/2) ) }}}
(2) {{{ -d = 20*(9/2) - 96 }}}
(2) {{{ -d = 90 - 96 }}}
(2) {{{ -d = -6 }}}
(2) {{{ d = 6 }}}
OK