How long does it take to beat the addiction of speed?

This mostly depends on the person. Some people can take amphetamines their whole life and never get addicted, while others might find themselves addicted after only a few uses. In general, about 17% of people who try amphetamines end up addicted at some point.

Also, it seems that either you are susceptible to addiction or you aren't, and this predisposition is mostly hereditary. People who aren't susceptible probably won't become addicted even if they take the drugs for a long time. If you are susceptible you won't necessarily become addicted, but the more you take the drug, the greater the risk.

Amphetamines are relatively addictive compared to other drugs - i.e. a greater percentage of people are prone to addiction, and the addiction happens faster if it does happen. For comparison, 10-12% of people who get drunk at some point go on to become alcoholics, while as many as 75% of people who try tobacco end up smokers.

These numbers are from one study, and they seem accurate to me based on personal experience, but there is a lot of controversy around this issue in the scientific community and good, unbiased research is very hard to find.