[填空题]
A tabletop water purifv kg/5rpeuq ph.nm8k/cr lq j. n89f-a0rsa 5/ie8 3em0 i5h avf)fuder;r is filled with 2500 $\mathrm{ml}$ of water. It takes the purifier 90 seconds to filter 900 $\mathrm{ml}$ of water.
The volume of water, V $\mathrm{ml}$ , remaining unfiltered in the purifier after t seconds, can be modelled by the differential equation
$\frac{\mathrm{d} V}{\mathrm{~d} t}=-q \sqrt{V}$,
where q is a positive constant.
1. Show that V=$\left(50-\frac{t}{9}\right)^{2}$ .
2. Find the time it takes for the purifier to filter all the water.
t= .
