My battery's just holding a 30mins charge and I was looking for a way to improve that. After a little bit of research I've got several doubts that I don't manage to understand:

1.- I've seen that the original es 11.1V with a capacity of 3600mAh (or 40Wh) and then, according to the HP specs it seems it can last 4.5h, which makes you assume that it could run on around 9Watts per hour (40Wh/4.5h)

My doubt now is that when I've checked the charger I've seen that it says 18.5V, 3.5A, so I'm understanding that its required input is 18.5V*3.5A=65W?? It's my understanding that this power will be used to run the laptop and to charge the battery, but if the laptop can run on ~9W, isn't it too much to input 65W?

2.- Will this 10000mAh Multi-voltage 5V / 9V / 12V 2A External Battery Pack be able to make it work? I know the Amps coming from the external AC are 3.5A but I was thinking along the lines of:
"If the laptop can run from the battery with 9Watts @11.1V, then that means it needs 9W/11.1V= 0.8A, so this device should be enough, as I think it can provide 1A or 2A at 12V for example".

I'm pretty lost in things I'm assuming, so maybe I'm saying something pretty stupid that it's not correct :). So looking forward to understand it though... It's kind of a hassle at the moment...hehehe

Many thanks!