The weather during Smedley's vacation was strange
-- It was cloudy on 13 different days but it was never cloudy for an entire day
-- Cloudy mornings were followed by clear afternoons
-- Cloudy afternoons were proceded by clear mornings
---There were 11 clear mornings and 12 clear afternoons in all
How long was the vacation?
To determine the length of Smedley's vacation, we need to analyze the given information about the weather conditions. Let's break it down step by step:
1. It was cloudy on 13 different days but never cloudy for an entire day. This means that there were partial cloudy days, where some part of the day was cloudy, but there were no full days of continuous cloudiness.
2. Cloudy mornings were followed by clear afternoons, and cloudy afternoons were preceded by clear mornings. This indicates a pattern where the weather changes from cloudy to clear or clear to cloudy during the day.
3. There were 11 clear mornings and 12 clear afternoons in total. This information suggests that there were more clear afternoons than clear mornings during the vacation.
Based on these clues, we can make some deductions:
- Since there were more clear afternoons than clear mornings, it means that some of the cloudy mornings turned into clear afternoons.
- Since there were 11 clear mornings and 12 clear afternoons, we can infer that there was at least one day where a clear morning turned into a cloudy afternoon.
Now, let's try to piece together the information:
- We know that it was cloudy on 13 different days, so at least 13 days were partially cloudy.
- Each partially cloudy day must consist of either a clear morning followed by a cloudy afternoon or a cloudy morning followed by a clear afternoon.
- If there were no partial cloudy days where it was clear in the morning and cloudy in the afternoon, then there must be 13 partial cloudy days where it was cloudy in the morning and clear in the afternoon.
- In this case, there must have been one clear morning that turned into a cloudy afternoon.
Now, the total number of days would be the sum of the partially cloudy days (13) and the clear morning turned cloudy afternoon day (1), which gives us 14 days.
Therefore, Smedley's vacation was 14 days long.