Problem Solving

In a certain bathtub, both the cold water and the hot water fixtures leak. The cold water leak alone will fill an empty bucket in c hours, and the hot water leak would fill the same bucket in h hours, where c < h. If both fixtures began to leak at the same 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. c/2 < t < h/2

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

ans E
Can someone please give the explanation

In this one, you will want to assign values. So from the given information we know that C<H which means that the cold water bucket will be filled quicker than the hot water. Lets say C=1 and H=2

Knowing this the formula says that if both were going at their constant rates, it would take t hours. T has to be less than C and H as both are filling the bucket. t= .66 when bucket c fills in 1 hour and bucket h fills in 2
so
I) 0 < .66 <2 = true
II) 1 <.66 <2 = false
III) 1/2 < .66 < 2/1 = True

Ans. = E