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. c/2 < t < h/2
A) I only
B) II only
C) III only
D) I and II
E) I and III - Answer
I picked numbers for c (3 hours) and h (6 hours); then, I found t (2 hours) and got my answer that way. Is there a better, more systematic way for solving this type of work problem?