At noon three students, Abby, Ben, and Cassie, are standing so that Abby is \(100\) m west of Ben and Cassie is \(160\) m east of Ben. While Ben stays in his initial position, Abby begins walking south at a constant rate of \(20\) m/min and Cassie begins walking north at a constant rate of \(41\) m/min.

In how many minutes will the distance between Cassie and Ben be the twice the distance between Abby and Ben?