You are at 8000 ft when 20 miles from the beacon.
You want to be at 1000 ft when 5 miles from the beacon.
So you need to lose 7000 ft while flying a distance of 15 miles.
At 150 kts you will take 15/150 = 0.1 hours (which is 6 minutes) to fly the 15 miles.
So you need to lose 7000 ft in 6 minutes.
Required ROD = 7000 ft / 6 mins = 1167 ft/min.
And from your post
7000/150 x 60 = 2400ft should read 7000 / 150 x 60 = 2800ft