Question 1023723
Time spent shopping is not travel time, so
{{{ 8 - 2 = 6 }}} hrs travel time
Let {{{ d }}} = distance to shopping mall
Let {{{ t }}} = time in hrs to get to shopping mall
{{{ 6 - t }}} = time in hrs to back from shopping mall
-----------------------------------------
Going to the mall:
(1) {{{ d = 50t }}}
Coming back from the mall:
(2) {{{ d = 25*( 6 - t ) }}}
-------------------------
By substitution:
(2) {{{ 50t = 25*( 6 - t ) }}}
(2) {{{ 50t = 150 - 25t }}}
(2) {{{ 75t = 150 }}}
(2) {{{ t = 2 }}}
Plug this result back into (1) or (2)
(1) {{{ d = 50t }}}
(1) {{{ d = 50*2 }}}
(1) {{{ d = 100 }}}
The shopping mall is 100 mi away
-----------------
check:
(2) {{{ d = 25*( 6 - t ) }}}
(2) {{{ d = 25*( 6 -2 ) }}}
(2) {{{ d = 25*4 }}}
(2) {{{ d = 100 }}}
OK