Question 885668
Let {{{ d }}} = distance Bret had traveled 
at {{{ 15 }}} mi/hr
Let {{{ t }}} = time spent traveling at
{{{ 15 }}} mi/hr
{{{ 80 - d }}} = distance Bret traveled at 
{{{ 10 }}} mi/hr
{{{ 5.5 - t }}} = time spent traveling at 
{{{ 10 }}} mi/hr
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Equation for riding at 15 mi/hr:
(1) {{{ d = 15t }}}
Equation for riding at 10 mi/hr
(2) {{{ 80 - d = 10*( 5.5 - t ) }}}
(2) {{{ 80 - d = 55 - 10t }}}
(2) {{{ d - 10t = 25 }}}
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Substitute (1) into (2)
(2) {{{ d - 10t = 25 }}}
(2) {{{ 15t - 10t = 25 }}}
(2) {{{ 5t = 25 }}}
(2) {{{ t = 5 }}}
(1) {{{ d = 15t }}}
(1) {{{ d = 15*5 }}}
(1) {{{ d = 75 }}}
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Bret had ridden 75 mi at 15 mi/hr
check:
{{{ 80 - d = 80 - 75 }}}
{{{ 80 - d = 5 }}}
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(2) {{{ 80 - 75 = 10*( 5.5 - 5 ) }}}
(2) {{{ 5 = 10*.5 }}}
(2) {{{ 5 = 5 }}}
OK