Can average speed ever be equal to instantaneous speed?

Hello!

Yes, instantaneous speed and average speed can be equal (and can be different).

The simplest case is when a body has a constant speed. In this case, its instantaneous speed is the same at any moment and the average speed over any time interval has the same value.

If the instantaneous speed was changed over some time interval, then the average speed over this interval is equal to the instantaneous speed at at least at one moment, maybe many. The reason for this is that speed is continuous and the average speed is between the least and greatest values of the instantaneous speed. This is an application of the intermediate value theorem.

If, for example, a body moves with a constant nonzero acceleration, then the average speed over any interval will have one and only one coincidence with the instantaneous speed on this interval.