Question 1158409
Let {{{ d }}} = the distance the slower one travels
{{{ 375 - d }}} = the distance the faster one travels
Let {{{ t }}} = the time the slower one travels
{{{ 9 - t }}} = the time the faster one travels
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(1) {{{ d = 40t }}}
(2) {{{ 375 - d = 45*( 9 - t ) }}}
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(2) {{{ 375 - d = 405 - 45t }}}
(2) {{{ d = 45t - 30 }}}
Substitute (1) into (2)
(2) {{{ 40t = 45t - 30 }}}
(2) {{{ 5t = 30 }}}
(2) {{{ t = 6 }}}
and
{{{ 9 - t = 3 }}}
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The slower one travels for 6 hrs
The faster one travels for 3 hrs
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check:
(1) {{{ d = 40t }}}
(1) {{{ d = 40*6 }}}
(1) {{{ d = 240 }}}
and
(2) {{{ 375 - d = 45*( 9 - t ) }}}
(2) {{{ 375 - d = 45*( 9 - 6 ) }}}
(2) {{{ 375 - d = 45*3 }}}
(2) {{{ d = 375 - 135 }}}
(2) {{{ d = 240 }}}
OK