Question 682308
First, you need to know how much of
a head start the freight train got
{{{ d[1] = 60*(1/2) }}}
{{{ d[1] = 30 }}} mi
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Now start a stopwatch when the passenger 
train leaves the station. Both trains will now
travel for the same amount of time {{{ t }}}
until they meet.
Let {{{ d }}} = the distance that the passenger
train travels until they meet
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freight train's equation:
(1) {{{ d - 30 = 60t }}}
passenger train's equation:
(2) {{{ d = 72t }}}
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Substitute (2) into (1)
(1) {{{ 72t - 30 = 60t }}}
(1) {{{ 12t = 30 }}}
(1) {{{ t = 2.5 }}}
The passenger train takes 2.5 hrs to catch the freight train
check answer:
(2) {{{ d = 72*2.5 }}}
(2) {{{ d = 180 }}}
and
(1) {{{ d - 30 = 60*2.5 }}}
(1) {{{ d - 30 = 150 }}}
(1) {{{ d = 180 }}}
OK
Note that the freight train covers {{{ 180 - 30 = 150 }}} mi
in the same 2.5 hrs that the passenger train goes {{{ 180 }}} mi