OK, what they mean is to assume that the deceleration is the same in both scenarios  i.e., 'a' is constant. So from v_2^2 v_1^2 = 2ad, you can see that if v_i is doubled, and v_2 is zero, d is quadrupled. From v_2 = v_1 + at, if v_2 is doubled then t is doubled.
