Speed limits are not widely observed anywhere in Peru, but for what it's worth, the "official" limit on most of the Panamericana is 100 km/h. As noted by opushomes, intercity buses are particularly bad about obeying the limit and it shows in their accident statistics. They are downright menaces.

In urban areas, the (unposted) limit is generally 35 km/h, with higher (posted) limits on major arterials.

When driving in Lima, you can safely ignore the 35 kph limit. However, if you're driving along the Panamericana, be careful as you enter towns along the highway, which in many places forms the main street of the town. On entering these towns the limit abruptly changes from 100 to 35, but this is not always well signed, and sometimes not signed at all. But with or without signage, the police sometimes wait to catch speeders, and wealthy gringos driving flashy SUVs are a favorite target.

If you get caught, make sure you have your driver's license handy and that you don't have to flash a cash-full wallet to get it out. Cooperate with them and be patient, to the point of agreeing that you were speeding and agreeing to pay the ticket. Inevitably, just before writing out the ticket, the cop will ask you to pay "directly to the municipality", or will just come flat out and ask for money for fuel for his truck, or beer. At that point, offer the guy S/.5.00 or S/.10.00, and you're home free.

Oh, and if you speak Spanish, it might be better to pretend you don't. "No espaņol" should do the trick.