The aircraft is travelling at 300 knots, i.e. 5 NM per minute.

One minute before the overhead the aircraft is 5 NM GROUND Range from the beacon.

The aircraft is flying at FL300, roughly 5 NM.

The right-angled triangle that is formed by height (5 NM) and GROUND Range (5 NM) has a hypotenuse which forms the SLANT Range, which is the DME Range.

DME Range^2 = Ground Range^2 + Height^2

DME Range^2 = 5^2 + 5^2

DME Range^2 = 25 + 25

DME Range^2 = 50

DME Range = Square Root 50

DME Range = 7.1 NM


As the aircraft approaches the beacon, the accuracy of the Groundspeed displayed reduces and under-reads.

Therefore, the DME Range will be 7.1 NM and the GS will be slightly less than 300 knots.