Question 996614
Since A has to travel the greater distance, I 
would giveA a head start {{{ t[1] }}}
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Let A's travel time = {{{ t + t[1] }}}
B's travel time = {{{ t  }}}
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A's equation:
(1) {{{ 30 = 50*( t + t[1] ) }}}
B's equation:
(2) {{{ 50 - 30 = 50t }}}
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(2) {{{ 20 = 50t }}}
and
(2) {{{ t = 20/50 }}}
(2) {{{ t = .4 }}}
and
(1) {{{ 30 = 50*.4 + 50t[1] }}}
(1) {{{ 50t[1] = 30 - 20 }}}
(1) {{{ 50t[1] = 10 }}}
(1) {{{ t[1] = .2 }}}
{{{ t + t[1] = .4 + .2 = .6 }}}
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{{{ .6*60 = 36 }}} min
{{{ .4*60 = 24 }}} min
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A must start out 36 min before 7 PM, or 6:24 PM
B must start out 24 min before 7 PM, or 6:36 PM
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Note that A gets a 12 min head start
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check:
(1) {{{ 30 = 50*( t + t[1] ) }}}
(1) {{{ 30 = 50*( t +.2 ) }}}
(1) {{{ t + .2 = .6 }}}
(1) {{{ t = .4 }}}
OK