Question 845917
Let {{{ t }}} = time in hrs spent on mountain roads
{{{ 5 - t }}} = time in hrs spent on highway
Let {{{ s }}} = motorist's speed in mi/hr on mountain roads
{{{ 3s }}} = motorist's speed in mi/hr on highway
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For mountain roads:
(1) {{{ 50 = s*t }}}
For highway:
(2) {{{ 150 = 3s*( 5 - t ) }}}
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(2) {{{ 150 = 15s - 3s*t }}}
Substitute (1) into (2)
(2) {{{ 150 = 15s - 3*50 }}}
(2) {{{ 150 = 15s - 150 }}}
(2) {{{ 15s = 300 }}}
(2) {{{ s = 20 }}}
and
{{{ 3s = 60 }}}
The motorist's rate on the highway was 60 mi/hr
check:
(1) {{{ 50 = s*t }}}
(1) {{{ 50 = 20*t }}}
(1) {{{ t = 2.5 }}}
and
(2) {{{ 150 = 3s*( 5 - t ) }}}
(2) {{{ 150 = 60*( 5 - t ) }}}
(2) {{{ 150 = 300 - 60t }}}
(2) {{{ 60t = 150 }}}
(2) {{{ t = 15/6 }}}
(2) {{{ t = 2.5 }}}
OK