Four times as much work. 4 times as much stopping distance.
Work Step by Step
The work needed is the change in kinetic energy. Kinetic energy scales as the square of the speed, so if the speed is doubled, KE is quadrupled. The amount of stopping force multiplied by the distance is the KE, so for the same force, the distance goes up by a factor of 4. This is discussed on pages 114-115.