Problem about Rain

Date: 09/20/2000 at 22:55:06
From: Melissa Bailey
Subject: Problem about rain

During a recent span of time, 11 days had some rain. A morning rain 
was always followed by a clear afternoon, and an afternoon rain was 
preceded by a clear morning. In all, nine mornings and 12 afternoons 
were clear. How many days had no rain at all?

I have no idea where to start.

Date: 09/21/2000 at 12:47:27
From: Doctor Rick
Subject: Re: Problem about rain

Hi, Melissa.

Start by thinking through what you know, and what you don't know.

We have some unknown total number of days. It rained on 11 of those 
days. It didn't rain on the others, and this latter number is what you 
are asked to find.

You know that it never rains both morning and afternoon of the same 
day. If it rains in the morning, it won't rain in the afternoon. If it 
rains in the afternoon, it didn't rain that morning.

You know that there were 9 mornings without rain, and 12 afternoons 
without rain.

How do we put this information together? Here's a question: how many 
different kinds of day could there be?

-- No rain
-- Rain in morning              \ rain sometime
-- Rain in afternoon            /
--------------------------------
Total number of days

Pick one of these and define it as a variable. Then see if you can 
write expressions for the others using that variable. I'll start. You 
might define

  x = days without rain

since that's what we want to find. Then you can start filling in the 
table:

-- No rain               x
-- Rain in morning       ?     \ rain sometime   11
-- Rain in afternoon     ?     /
--------------------------------
Total number of days    11+x

Why is the total number of days equal to 11+x? Because it rained on 11 
days, and the total is the sum of the days without rain and the days 
with rain.

See what you can do to finish the table. Then you can write an 
equation in x, and solve it to answer the question.

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/