**Solution:**

**Approach:-**

we could express volume in the SI Using the dimensions of eigther $\mathrm{m}^3$ or $L$.
So, we initially decide to Convert volume to liters with the Conversion factor 1 gal $=3.785 \mathrm{~L}$.
**Solution:-**
Converting dimensions for both volume and time.
$
\begin{aligned}\
q &=\left(10 \frac{\mathrm{gal}_{\mathrm{m}}}{\mathrm{min}}\right)\left(\frac{1}{60} \frac{\mathrm{min}}\{\mathrm{s}}\right)\left(3.785 \frac{\mathrm{L}}{gal}\right) \\
&=0.6308\left(\frac{\mathrm{gaL}}{\mathrm{min}}\right)\left(\frac{\mathrm{min}}{\mathrm{s}}\right)\left(\frac{1}{gal}\right) \\
&=0.6308 \mathrm{Ls}^{-1}\
\end{aligned}\
$
**Discussion:-**
However, since a cubic meter is 1000 times larger then a liter,
The dimension $L / 9$ turns out to be better suited for the problem at,
$
q=0.6308 \frac{L}{S}\
$