Question 644082
The 60 mi/hr train has a 1 hr head start
{{{ d[1] = 60*1 }}}
The head start is {{{ d[1] = 60 }}} mi
Let {{{ d }}} = distance that 60 mi/hr train travels
after stopwatch starts until they meet
Let {{{ t }}} = time in hrs on stopwatch after 
50 mi/hr train leaves
---------
Start a stop watch when the 50 mi/hr train leaves.
They both will now travel for the same amount
of time. 
---------
60 mi/hr train's equation:
(1) {{{ d = 60t }}}
50 mi/hr train's equation:
(2) {{{ 500 - ( d + 60 ) = 50t }}}
-----------------------
Substitute (1) into (2)
(2) {{{ 500 - ( 60t + 60 ) = 50t }}}
(2) {{{ 500 - 60t - 60 = 50t }}}
(2) {{{ 110t = 440 }}}
(2) {{{ t = 4 }}}
4 hours after the 50 mi/hr train leaves Charleston
they will meet
check:
(1) {{{ d = 60*4 }}}
(1) {{{ d = 240 }}}
and
(2) {{{ 500 - ( d + 60 ) = 50*4 }}}
(2) {{{ 500 - d - 60 = 200 }}}
(2) {{{ d = 500 - 60 - 200 }}}
(2) {{{ d = 240 }}} 
Note that 240 + 200 + 60 = 500 as it should