As mentioned above it's simple enough to guess the average of how long it will take before the book wears off. Since the xp boost is 50% and the rested boost is 50%, if you are getting 400 xp a cut then you're getting 100xp from using the book. Though is it really that long for it to wear off? 9000/100=90 cuts, with maxed output you get 8 cuts per tree so the book should last about 11 nodes and 2 gathers. On average I'd say it takes about 15-25 mins to cuts 3 nodes based on the distance from one another so overall it would take about an hr to an hr and 30 minutes.

To be honest, I don't really see why you are even using the book at 47, it's not like you'll stop gathering once you hit 50 so why speed up the process? You're better off purchasing the manuals for crafting since the 9k from that is a lot more noticeable then the one for gathering. The manual for gathering is better off used from 40-45 since the leves offer a nice chunk of xp during those levels but once you hit 45+ the manuals themselves only offer a miniscule difference.

I'd say just save your seals if you find it that tedious to do 12 nodes to get rid of the book, justdo 6/6/6/6 daily and you'll be getting the same amount of xp but at least you won't be burning yourself out with forcing yourself to gather just so you can gain all of the 9k xp.

But again just remember
If boost is:
25=360 cuts/45 nodes
50=180 cuts/22.5 nodes
75=120 cuts/15 nodes
100=90 cuts/11.25 nodes
150=60 cuts/7.5 nodes
200=45 cuts/5.6 nodes
300=30 cuts/3.75 nodes