In a certain bathtub, both the cold-water and the hot-water fixtures leak. The cold-water leak alone would fill an empty bucket in c hours, and the hot-water leak alone would fill the same bucket in h hours, where c < h. If both fixtures began to leak at the same time into the empty bucket at their respective constant rates and consequently it took t hours to fill the bucket, which of the following must be true?
I. $$0 \lt t \lt h$$
II. $$c\lt t\lt h$$
III.$$ \frac{c}{2}\lt t \lt \frac{h}{2}$$