Ask HN: How fast is an AWS auto scaling group?

I have been struggling to find an answer to this simple question. What is the rate at which new instances can be created in an autoscaling group?

Let's say if there is a sudden spike in traffic, and I need to go from 50 EC2 instances to 300. How long would it take (lets assume a pre-baked AMI). If every EC2 takes x minutes to start up, in how much time will my auto scaling group achieve the target size? Will all 250 instances be started up in parallel ?