The best way to solve the problem is to consider the objects leaving from rest at 2 different heigths H1 and H2 such that H1/H2=2 (basically condider the case of dropping two obejects from different heights). You can use the formula for diplacement for each case, take a ratio between these two quantities and find a ratio in terms of time. Remember that if you drop the objects the initial velocity was zero (all what you need to know is just the initial height, in this case just the ratio of the heights).