An empty pool being filled with water at a constant rate takes hours to fill 3/5 of its capacity. How much more time will it take to finish filling the pool?
Let's look at the first step of your solution, keeping in mind the units of the quantities:
3/5 pools * 8 h = 24/5 pools*h
At this point, we have a unit that doesn't really help us in the question. We need to figure out how long it takes to fill up 2/5 of the pool, which we could write in the form
x hr / (2/5 pools)
As you can see, here, we're dividing the terms, not multiplying them. And to be able to use the information given in the problem, we need to put it in this form. For example:
8 hr / (3/5 pools) = 13 1/3 hr/pool
And now, we can solve for x above:
x hr / (2/5 pools ) = 13 1/3 hr / pools
x hr = (13 1/3 hr)*(2/5 pools)/ pools
x hr = 5 1/3 hr = 5 hr 20 min
1 Explanation