Let t be the time (in hours) for patrol car to catch up the bus.

    // The time counts starting from 1:30 pm.


To the catching moment, the bus will be in move (t + 0.5) hours, 
or 0.5 hours more than the patrol car.


In t hours, the patrol car covers the distance 80*t miles.

In (t+0.5) hours, the bus covers the distance of 60*(t+0.5) miles.


The distance is the same at the catching moment:


    80t = 60(t+0.5)

    80t = 60t + 30

    80t - 60t = 30

    20t = 30

      t =  =  hours =  hours = 1 hour and 30 minutes.


The patrol car will catch the bus in 1 hour and 30 minutes after 1:30 pm, i.e. at 3:00 pm.    ANSWER


It will happen at the distance   = 120 kilometers from the rest stop.       ANSWER