The passenger train will take 2.5 hours to catch the freight train.
Explanation
Suppose, it will take [tex]t[/tex] hours for the passenger train to catch the freight train.
As the passenger train leaves the station after 30 minutes or [tex]\frac{1}{2}[/tex] hour , so the freight train will travel the same distance as the passenger train in [tex](t+\frac{1}{2})[/tex] hours.
Speed of the freight train is 60 mph and speed of the passenger train is 72 mph.
As [tex]Distance = Speed*Time[/tex] , so the equation will be......
[tex]72t= 60(t+\frac{1}{2})\\ \\ 72t= 60t+30\\ \\ 12t=30\\ \\ t= \frac{30}{12}=2.5[/tex]
So, the passenger train will take 2.5 hours to catch the freight train.
