Problem about RainDate: 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/ |
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