Question 230087
In 30 min, the freight train has gone:
{{{d = 60*(1/2)}}} mi
{{{d = 30}}} mi (it's headstart)
When the passenger train leaves the station, I start a stopwatch
and I'll stop it at time = {{{t}}} when trains meet
Let {{{d[p]}}} = distance the passenger train has to
go to catch freight train
For passenger train:
(1) {{{d[p] = 72t}}}
For freight train:
(2) {{{d[p] - 30 = 60t}}}
Substitute (1) in (2) 
{{{72t - 30 = 60t}}}
{{{12t = 30}}}
{{{t = 5/2}}}
The passenger train catches the freight train in 2.5 hrs
check:
(1) {{{d[p] = 72t}}}
{{{d[p] = 72*2.5}}}
{{{d[p] = 180}}} mi
and
(2) {{{d[p] - 30 = 60t}}}
{{{d[p] = 60*2.5 + 30}}}
{{{d[p] = 150 + 30}}}
{{{d[p] = 180}}} mi
OK