You'd do a lot better with a standard high velocity fan (also 35 bucks, and you can get them cheaper): http://www.northerntool.com/shop/tools/product_200361823_200...
You want to be changing the air at a much higher rate than they are.
They quote a 13.5 square meter bedroom. This is 145.313 square feet. If they have 8 foot high ceilings, it's 1160 cubic feet.
In order to be changing the air so little as they are, my guess is this box fan is ~40CFM, giving ~30 minutes between air changes.
For 30 bucks, you can get a 2000+ CFM fan (see above), and put the filter on the intake side rather than the output side. This would change the air in the room roughly twice a minute, or roughly 60 times faster. There will be some loss of CFM due to static pressure increase, but ...
They also probably want a cheap, washable, electrostatic pre-filter so you aren't wasting the filtrating on easily caught particles. Otherwise, you are just going to go through this hepa filter really quickly.