The first thing you need to keep in mind is that most POSes can't be taken down in one operation. If the tower is stronted (most are) it will enter reinforced, rendering it invulnerable, once it hits 25% shields. When the timer is up the tower becomes vulnerable once more, and you can take it down (shields, armor, structure).

See this post for more details on reinforced mode.

How long it takes to take down a POS really depends on a lot of factors. Your fleets DPS, resistances of the POS etc. A large POS has 35-50 mill shield HP depending on race. A medium POS has 17.5-25 mill shield HP. A small POS has 8.75-12.5 mill shield HP. Shield is the major barrier to get through and once it is down armor and structure fold relatively quickly. As a side note, the shield recharge rate on all towers is negligible.

Armor values range from 10 mill HP on a large Amarr tower to 1 mill HP on a small Caldari tower. All armor resistances are 0%.

Structure HP varies between 10 mill HP on a large Gallente and 1 mill HP on a small Caldari tower. It is also worth mentioning that the 99% structure resists (for tower and mods) are only active while the force field is operational. The force field drops and the POS goes offline as soon as it is out of armor. This means that when you actually start damaging the tower hull, it has no resists at all.

As you can see it's hard to give a definite answer to how long it takes to kill a POS. You'll have to look at the POS and take note of it's HP (taking into account any hardeners) and compare this to your fleets DPS.

In general it is pretty hard to take down a large POS without Dreadnoughts. It can be done, but takes a long time. A small and medium POS can be taken down without too much issue, by a reasonably sized BS fleet.

Example:
You want to take down a small Minmatar tower. The POS is not equipped with any hardeners. The tower has 11.250.000 shield HP and the resistances are 50% EM, 0% TH, 0% KI, 25% EX.

You have 5 battleships each dealing 500 DPS. To make things easier, lets assume your fleet is dealing exclusively EM damage.

To put the POS into reinforced mode you will have to go through 75% of its shields, reducing it to 25%. This means you'll have to shoot through 8.437.500 HP of shield before the POS is reinforced. Your fleets total DPS is 5*500=2500. This is cut in half by the EM resist, making your effective DPS 1250.

The time it takes to put the POS in reinforced is 8.437.500/1250=6750 seconds, or 112.5 minutes. Almost two hours.

Assuming no shield repair has occurred we are looking at ~25% shields remaining when the POS comes out of reinforced. This means we the tower has 2.812.500 shield HP remaining. The tower also has 1.5mill armor HP and 1.5mill structure HP.

Using the same 5 BS working through the remaining shields will take 2.812.500/1250=2250 seconds. Working through armor and structure we are back at full damage due to the lack or resistances. Time to kill armor and structure is (1.500.000+1.500.000)/2500=1200 seconds. This gives us a total of 2250+1200=3450 seconds for the killing of the tower. Roughly 57.5 minutes.

Based on this we can see that killing a small Minmatar POS takes 5 battleships a total of almost 3 hours, split over two days.