All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Nice Weather (Posted on 2004-11-02) Difficulty: 2 of 5
During a certain period of days in Cucumberland recently it was observed that when it rained in the afternoon, it had been clear in the morning, and when it rained in the morning, it was clear in the afternoon. (In a given morning or afternoon, it is either raining or it is clear.) It rained on 100 days, and was clear on 19 afternoons and 95 mornings. How many days were there altogether?

No Solution Yet Submitted by SilverKnight    
Rating: 4.0000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Linear algebra solution | Comment 4 of 11 |

There are only 3 types of days:

A = rain morning, clear afternoon

B = clear morning, rain afternoon

C = clear all day  (It is clear from the problem that it can't rain all day)

The info in the problem yields a system of 3 equations

(1) A+B=100; (2) B+C=95; (3) A+C=19

What we want is A+B+C so we only need one of the variables.

Subtracting (2) from (1) yields (4) A - C = 5

Adding (4) and (3) yields 2A = 24 so A=12

This and (2) gives the solution: A + B + C = 12 + 95 = 107

-Jer


  Posted by Jer on 2004-11-02 17:11:29
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (3)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information