Question 880936
Let {{{ d }}} = the distance in miles for the run
{{{ 121 - d }}} = the distance in miles for the bicycle race
Let {{{ t }}} = the time in hrs for the run
{{{ 6 - t }}} = the time in hrs for the bicycle race
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Equation for the run:
(1) {{{ d = 6t }}}
Equation for the bicycle race:
(2) {{{ 121 - d = 23*( 6 - t )  }}}
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(2) {{{ 121 - d = 23*6 - 23t }}}
(2) {{{ 121 - d = 138 - 23t }}}
(2) {{{ 23t - d = 138 - 121 }}}
(2) {{{ 23t - d = 17 }}}
Substitute (1) into (2)
(2) {{{ 23t - 6t = 17 }}}
(2) {{{ 17t = 17 }}}
(2) {{{ t = 1 }}}
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Substitute this result back into (1)
(1) {{{ d = 6t }}}
(1) {{{ d = 6*1 }}}
(1) {{{ d = 6 }}}
and
{{{ 121 - 6 = 115 }}}
The bicycle race is 115 mi
check:
(2) {{{ 121 - d = 23*( 6 - t )  }}}
(2) {{{ 121 - 6 = 23*( 6 - 1 )  }}}
(2) {{{ 115 = 23*5 }}}
(2) {{{ 115 = 115 }}}
OK