Question 621152
Let {{{ t }}} = time traveled by car
{{{ 1 - t }}} = time traveled by motorcycle
Let {{{ d }}} = distance traveled by car
{{{ 27 - d }}} = distance traveled by motorcycle
--------
By car:
(1) {{{ d = 31t }}}
By motorcycle:
(2) {{{ 27 - d = 25*( 1 - t ) }}}
-----------------------
Substitute (1) into (2)
(2) {{{ 27 - 31t = 25*( 1 - t ) }}}
(2) {{{ 27 - 31t = 25 - 25t }}}
(2) {{{ 6t = 2 }}}
(2) {{{ t = 1/3 }}}
{{{ (1/3)*60 = 20 }}}
Ashley traveled 20 minutes by car
check:
(1) {{{ d = 31*(1/3) }}}
(1) {{{ d = 31/3 }}}
and
(2) {{{ 27 - d = 25*( 1 - 1/3 ) }}}
(2) {{{ 27 - d = 25*(2/3) }}}
(2) {{{ 81 - 3d = 50 }}}
(2) {{{ 3d = 31 }}}
(2) {{{ d = 31/3 }}}
OK