Would this ventilation system cut it?

Hello!

I have a grow box, which is about 45 cubic feet in size. I am running a 250W HPS inside it, but I will definately need a carbon filter soon. So I'm looking into upgrading my fan, as the duct-booster probably won't cut it.

The thing is, the fan has to pull through the filter, and then push into about.. 15 feet of ducting, with 3x 90° bends. I was wondering if a 165 CFM fan like this one would be enough for this?:

http://www.hydroponics.eu/fans-and-filters-c-29/extractor-fans-s-79/winflex-biturbo-12-5cm-280m3hour-9397.html

I WILL NOT BE BUYING FROM THE SITE I LINKED AS I'VE HEARD SOME NEGATIVE REVIEWS ABOUT IT. BEAR IN MIND. I'm simply using this site because it's in English and has a lot of different products listed on it.

Now.. What I'm wondering - would this fan be strong enough and is it even the right type of fan for what I'm trying to do? If it isn't, what should I be looking at?

Thank you all in advance

Hi. This fan havent got much static pressure. I prefer http://www.ebay.com/itm/CAP-Valuline-4-Centrifugal-Fan-171-CFM-inline-vortex-4-exhaust-blower-/120895660400?pt=LH_DefaultDomain_0&hash=item1c25f16170 (it is better pull air. good for carbon filter ) or http://www.ebay.com/itm/Dayton-115V-1-54-1-45A-1-40HP-Blower-4C006B-/331553274001?pt=LH_DefaultDomain_0&hash=item4d321d7891 (it is better pushing air. good for lights cooling. Id draw more power, but have got more static pressure, and moves more air quitly)

Hey! Thank you for the reply. After some further reading, I decided to go for the following fan and appropriate filter:

https://www.maxgrowshop.com/en/air-extractor-fans/759-fan-pk125-mes-420m3-h.html

Seemed like a good price for it, so, hope it does what it's supposed to!