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As a lover of rules, I hated not having an answer to "If a character has a BAB of +6/+1 because she is a 6th level ranger, how many attacks per round does she get with a Longbow?"
Nothing states explicitely that a bow is as fast as a sword in our ranger's hands. HOWEVER, a few other items state how they are slower.
1. Crossbow descriptions list loading the weapons as move actions (light) or full round actions (heavy).
2. Rapid Reload feat (For crossbows) states "If you have selected this feat for a hand crossbow or light crossbow, you may fire that weapon as many times in a full-attack action as you could attack if you were using a bow." This implies you can fire a bow multiple times with a high BAB.
3. The Quickdraw feat states "A character who has selected this feat may throw weapons at his full normal rate of attacks (much like a character with a bow)."
4. Of final note: "Drawing ammunition for use with a ranged weapon (such as arrows, bolts, sling bullets, or shuriken) is a free action."
By what I see so far, it looks like a high level ranger (6 is high enough!) can make multiple attacks in a round with a longbow / shortbow. One with the right feats can make multiple attacks with a light crossbow.
So, what is the final answer? How many attacks can a level 6 ranger (BAB +6/+1) with no other applicable feats make in a round with a longbow?

Casual Viking |

2 attacks. A character with +6 BAB has 2 attacks, and nothing prevents him from taking both of them with his bow. And you should expect him to have both Rapid Shot and Manyshot at this point, for a total of 3 attacks of which the first one hits twice (manyshot is weird).
To preemptively answer a related question, there is difference between +6 BAB from one class and a total of +6 BAB from 2 or 3 different classes. The +6/+1 on the table is a reminder, not an actual rule; +6 BAB is +6 BAB.

GreyFox95 |

To preemptively answer a related question, there is difference between +6 BAB from one class and a total of +6 BAB from 2 or 3 different classes. The +6/+1 on the table is a reminder, not an actual rule; +6 BAB is +6 BAB.
http://www.d20pfsrd.com/gamemastering/combat#TOC-Attack-Bonus
The grey sidebar on this says otherwise.
Casual Viking |

2 attacks. A character with +6 BAB has 2 attacks, and nothing prevents him from taking both of them with his bow. And you should expect him to have both Rapid Shot and Manyshot at this point, for a total of 3 attacks of which the first one hits twice (manyshot is weird).
To preemptively answer a related question, there is difference between +6 BAB from one class and a total of +6 BAB from 2 or 3 different classes. The +6/+1 on the table is a reminder, not an actual rule; +6 BAB is +6 BAB.
Oh FFS. NO difference. There is NO difference between +6 from one source and +6 accumulated from different classes and HD. Damn fat fingers and tasty mead.