The rain was the important detail. Thanks for including that. The water will make the belt slip for a few seconds until it clears off. The pulleys being wet is not the issue. It is the build-up of excessive water The same thing has happened on my minivan two times because I have been too lazy to put a splash shield back on.
We do not get involved with costs here because there is too many variables. Quality and size affect the belt's price. A typical cost will run between ten and thirty dollars. Engine size is an important variable too. Most engines today use a spring-loaded tension-er pulley that really speeds the job up. Many belts can be replaced in just a few minutes. There are a few that get pretty involved and complicated. GM used to have a few that were designed only to go together quickly on the assembly line, with no regard for later. Some of those required removing an engine mount that the belt went around. Those can take over an hour to replace.
Serpentine belt failures are actually pretty rare. The common gauge for wear is to find more than one crack across the ribbed side in an inch of belt. Fewer than that is acceptable. If the belt shreds or is torn along one edge, there is a pulley that is tipped or turned, causing the side of the belt to rub against something. That is usually caused by the tension-er or an idler pulley with a worn bearing. Tipped or turned pulleys also are responsible for belt squeals. They cause the belt to slide across that pulley as it goes around it. We tend to ignore these belts until some other problem causes a failure, then worn parts and the belt typically get replaced at the same time.
Here are links to some related article you might find interesting:
https://www.2carpros.com/articles/chirping-noise
https://www.2carpros.com/articles/how-a-serpentine-belt-works
https://www.2carpros.com/articles/replace-serpentine-belt
There is more articles related to serpentine belts and noises in the "Engine" section on this page:
https://www.2carpros.com/articles
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Saturday, October 6th, 2018 AT 8:43 PM