Question 1024860
In 1 hour ( noon to 1 PM ), how far does the
1st train get?
{{{ d[1] = 44*1 }}}
{{{ d[1] = 44 }}} mi
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Start a stopwatch when the 2nd train leaves Charleston
Let {{{ t }}} = time on stopwatch in hours when 
the trains pass eachother
Let {{{ d }}} = distance in miles that the 2nd train
travels until they pass eachother
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Equation for the 1st train:
(1) {{{ 500 - 44 - d = 44t }}}
Equation for the 2nd train:
(2) {{{ d = 32t }}}
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Sustitute (2) into (1)
(1) {{{ 500 - 44 -32t = 44t }}}
(1) {{{ 456 - 32t = 44t }}}
(1) {{{ 76t = 456 }}}
(1) {{{ t = 6 }}}
6 hours after the train leaves Charleston  
the two trains pass each other
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check answer:
(2) {{{ d = 32t }}}
(2) {{{ d = 32*6 }}}
(2) {{{ d = 192 }}}
and
(1) {{{ 500 - 44 - d = 44t }}}
(1) {{{ 500 - 44 - d = 44*6}}}
(1) {{{ 500 - 44 - d = 264}}}
(1) {{{ d = 500 - 44 - 264 }}}
(1) {{{ d = 500 - 308 }}}
(1) {{{ d = 192 }}}
OK
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Note that in the 6 hrs, train 1 travels
{{{ 500 - 44 - 192 = 264 }}} mi 
and train 2 travels {{{ 192 }}} mi 
{{{ 264 + 192 = 456 }}}
and {{{ 456 + 44 = 500 }}}
total distance traveled by both