12. A pipe burst occurred in a low-lying area by the riverbank, and river water is continuously gushing out, assuming the water gushing out per minute is constant. If two water pumps are used to pump out the water, it takes 40 minutes to finish; if four water pumps are used, it takes 16 minutes to finish. If the water needs to be pumped out within 10 minutes, then at least $\qquad$ water pumps are required.
12.6 .

Let the amount of water that has already gushed out before the pumping starts be $u$ cubic meters, the rate of water gushing out per minute be $b$ cubic meters, and the amount of water each pump can extract per minute be $c$ cubic meters $(c \neq 0)$. From the given conditions, we have
$$
\left\{\begin{array}{l}
a+40 b-2 \times 40 a, \\
a: 16 b=4 \times 16
\end{array}\right\}\left\{\begin{array}{l}
a=\frac{160}{3} c, \\
b=\frac{2}{3}
\end{array}\right.
$$
The number of pumps is
$$
\frac{a+10 b}{10 c}=\frac{\frac{100}{3} c+\frac{20}{3} c}{10 c}=6 .
$$