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?
We can use the following equation to relate the number of painters, the area of the wall, and the time to paint the wall:
Painters * Time = Wall area / Paint rate
We know that 50 painters can paint a 3600 square foot wall in 20 minutes, so we can calculate the paint rate as follows:
Paint rate = Wall area / (Painters * Time) = 3600 sq ft / (50 painters * 20 minutes) = 7.2 sq ft/painter-minute
Now, we can use the paint rate to calculate the amount of time it would take for 25 painters to paint a 4000 square foot wall:
Time = Wall area / (Painters * Paint rate) = 4000 sq ft / (25 painters * 7.2 sq ft/painter-minute) = 22.2 minutes
Therefore, it would take 22.2 minutes for 25 painters to paint a 4000 square foot wall.