Work/Rate Problems

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. \(0 < t < h\)
II. \(c < t < h\)
III. \(\dfrac{c}{2} < t < \dfrac{h}{2}\)

A) I only
B) II only
C) III only
D) I and II
E) I and III

The OA is E

Source: GMAT Prep