All members of our painting team paint at the same rate. If $40$ members can paint a $100$ square foot wall in $50$ minutes, then how long would it take the $40$ members to paint a $500$ square foot wall, in minutes?
Since all $40$ members paint at the same rate, then in $50$ minutes, each member paints $\frac{100\text{ sq ft}}{50} = 2$ square feet. To paint a $500$ square foot wall, each member must paint $\frac{500}{2} = 250$ square feet. Each member can paint another $250$ square feet in $250/2 = \boxed{125}$ minutes.
