If 3/5 of the work is done in 8 hours, does that mean that I need to solve for the rate and plug that back in to get the time for the remaining 2/5 of the work? What is a quicker way to solve this problem.

Hi Mariela,

An alternative to solving for the rate (or to solving for the total time, as in the O.G. solution) would be to set up a comparison. Since the pool is filled at a constant rate, the rate of filling the first 3/5 of the pool is the same as the rate of filling the last 2/5 of the pool. Rate = Amount filled / Time, so:

Rate = (3/5 capacity) / 8 hours = (2/5 capacity) / x hours

Cross-multiply:
(3/5)(x) = (2/5)(8 hours)

Isolate x:
x = (2/5)(8 hours)(5/3)
x = (2/3)(8 hours)
x = 16/3 hours = 5 hours 20 minutes

Notice that this answer "makes sense." If the pool were 5 units in capacity, the amount filled so far is 3 units (3/5 of the capacity). There are 2 more units to go, which should take 2/3 as long as it did to fill the first 3 units. 2/3 of 8 hours is 5 hours 20 minutes.