Question of the Day #334 (1/9/10)

[Kazza]

The weather during Karen's holiday was all over the place. It rained on 15 different days, but it never rained for a whole day.

•Rainy mornings were followed by clear afternoons.
•Rainy afternoons were preceeded by clear mornings.
•There were 12 clear mornings and 13 clear afternoons in all.
•How long was the holiday?


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[bane]

andele, andele... PM sent :thumbup:

 

[SirIsaac]

PM sent...

 

[astpierre]

pm sent...

 

[wrlomas]

pm sent in the am

 

[lsherrer]

Pm on its way!

 

[FizzySix]

Too much rain for a vacation....

 

[Kazza]

The weather during Karen's holiday was all over the place. It rained on 15 different days, but it never rained for a whole day.

•Rainy mornings were followed by clear afternoons.
•Rainy afternoons were preceeded by clear mornings.
•There were 12 clear mornings and 13 clear afternoons in all.
•How long was the holiday?

5 totally clear days and 15 half and half.

In the 15 half and half days:
7 <= 12 of the clear mornings were followed by rain,

8 <= 13 of the clear afternoons were preceeded by rain.

20 days of the holiday.


Only one winner today, well done Sir Isaac :thumbup:

 

[SirIsaac]

Only one winner today, well done Sir Isaac :thumbup:

I wasn't expecting that!

Reasonably simple algebra, if there is any interest I can show my work.

 

[Kazza]

I wasn't expecting that!

Reasonably simple algebra, if there is any interest I can show my work.

Go for it



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[SirIsaac]

Go for it



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OK, you asked for it

Given information:
No days with all rain.
15 days with some rain.
12 days with clear morning, rain afternoon.
13 days with rain morming, clear afternoon.

Let x equal the number of days with clear mornings, and rainy afternoons
Let y equal the number of days with no rain at all
Let z equal the number of days with rainy mornings, and clear afternoons

So:
x + y = 12 (days with clear morinings)

y + z = 13 (days with clear afternoons)

x + z = 15 (days with rain)

Three equations, three unknowns.

solve for y in the first equation:

y = 12 - x

Substitute for y in the second equation:

(12 - x) + z = 13

simplifies to:
-x + z = 1

Add to the third equation:

x + z = 15
-x + z = 1
2z = 16
z = 8

Substitute value of z back into second equation:

y + 8 = 13
y = 5

Substitute value of y back into second equation:

x + 5 = 12
x = 7

So the holiday was 7 days with clear AM, rain PM plus 5 days with no rain plus 8 days with rain AM and clear PM, total 20 days.