Question 1080922
Let {{{ s }}} = the speed of the southbound train
{{{ s + 10 }}} = the speed of the northbound train
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What is the northbound station's headstart in miles 
when the southbound train leaves station?
{{{ d[1] = ( s + 10 )*3 }}}
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Start a stopwatch when the southbound train leaves station
and time both of the trains
Let {{{ d }}} = distance southbound train travels 
from 3 AM to 6 AM
{{{ ( s + 10 )*3 }}} is the distance northbound train
travels from 3 AM to 6 AM
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Equation for the southbound train:
(1) {{{ d = s*3 }}}
Equation for the northbound train:
(2) {{{ 330 - d - d[1]  = ( s + 10 )*3 }}}
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(2) {{{ 330 - d = 6*( s + 10 ) }}}
(2) {{{ 330 - d = 6s + 60 }}}
Plug (1) into (2)
(2) {{{ 330 - 3s = 6s + 60 }}}
(2) {{{ 9s = 270 }}}
(2) {{{ s = 30 }}}
and
{{{ s + 10 = 40 }}}
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The speed of the southbound train is 30 mi/hr
The speed of the northbound train is 40 mi/hr
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check:
(1) {{{ d = s*3 }}}
(1) {{{ d = 3*30 }}}
(1) {{{ d = 90 }}} mi
and
(2) {{{ 330 - d - ( s + 10 )*3  = ( s + 10 )*3 }}}
(2) {{{ 330 - d - ( 30 + 10 )*3  = ( 30 + 10 )*3 }}}
(2) {{{ 330 - d = 120 + 120 }}}
(2) {{{ d = 330 - 240 }}}
(2) {{{ d = 90 }}} mi
OK
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Hope I got it. Check the math & get a 2nd 
opinion if needed