Filling up your luxury pool

I had this question for homework a while ago. Since the bigger pipe finishes work 3 times faster than the smallest pipe and since the middle sized pipe finishes the work half as fast as the big pipe we just add up there rates over S (the smallest pipe) because that's what these rates are being compared to. So 3w/s +1.5w/s + 1w/s =1w/3h. Then 5.5w/s =1w/3h 5.5x3=16.5h

Yours is much simpler than mine. I did this: Let $w$ = the total work. Let's assume the large pipe does $\frac {1}{3} w / h$ . Then if this is one third the time of the smaller pipe, the smaller pipe does $\frac {1}{9} w / h$ . The medium pipe takes twice as long as the larger, which is $\frac {1}{6} w / h$ . If we add these all up we get the work done by all three per hour. After finding common denominator and adding we get total work done is $\frac {11}{18} w / h$ . Now, this job takes 3 hours, so multiply it by 3h and the pipes have done $\frac {33}{18} w$ . Simply divide this by the work done by small pipe per hour to find the time it takes the small pipe. $\frac {33}{18} w / \frac {1}{9} w / h = \frac{297}{18} h = \frac {16}{2} h = \boxed{16.5 h}$