All members of our painting team paint at the same rate. If $50$ members can paint a $3600$ square foot wall in $20$ minutes, then how long would it take for $25$ members to paint a $4000$ square foot wall, in minutes?
Since the painters work at the same rate, if we multiply the number of workers by $2$, we must multiply the time by $\frac{1}{2}$ to keep the amount of work the same. So, if $50$ members take $20$ minutes, then $100$ members would take $10$ minutes.
Now we need to take into account the fact that the number of workers does not divide evenly into the amount of work. Since we don't divide evenly, we get a remainder. The remainder is $25$ and our answer is $10+\frac{25}{100}=\boxed{10.25}$ minutes.