SOLUTION: It rained on exactly 11 days during Jane’s holiday trip. On each rainy day it rained either in the morning or in the afternoon but not both. There are
exactly 13 afternoons when
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exactly 13 afternoons when
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Question 287831: It rained on exactly 11 days during Jane’s holiday trip. On each rainy day it rained either in the morning or in the afternoon but not both. There are
exactly 13 afternoons when it did not rain and exactly 16 mornings when it did not rain. How many days did the trip last? Found 2 solutions by Theo, richwmiller:Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website! It rained exactly 11 days during Jane's trip.
When it rained, it rained in the morning or the afternoon but never both.
There are 13 afternoons when it did not rain.
There are 16 mornings when it did not rain.
How long was the trip?
The trip was 29 days long.
13 + 16 = 29.
The 11 days that it rained cannot be added to this total because:
If it rained in the afternoon, then the morning was clear and that day is already counted as a clear morning day.
If it rained in the morning, then the afternoon was clear and that day is already counted as a clear afternoon day.
Since there were less rainy days than either clear afternoon days or clear morning days, the rainy days could have all come from either pot or the rainy days could have come some from the clear morning pot and some from the clear afternoon pot.
Either way, the total was unchanged, and the total has to be 29.
Here's one way the days could look like:
You have to have 16 days that are clear in the morning and you have to have 13 days that are clear in the afternoon.
days 1 to 16 are clear in the morning (c).
days 17 to 29 are clear in the afternoon (c).
morning afternoon
1 c
2 c
3 c
4 c
5 c
6 c
7 c
8 c
9 c
10 c
11 c
12 c
13 c
14 c
15 c
16 c
17 c
18 c
19 c
20 c
21 c
22 c
23 c
24 c
25 c
26 c
27 c
28 c
29 c
Take any of those days and make them rainy in the afternoon or the morning depending on whether they are clear in the morning or afternoon.
You cannot add another day, because then you mess up the totals of clear mornings or clear afternoons.
You have to pick an existing day to make the other half of the day rainy.
There are many possible solutions. One of them would look like this:
morning afternoon
1 c r
2 c r
3 c r
4 c
5 c
6 c r
7 c r
8 c
9 c
10 c
11 c r
12 c
13 c r
14 c
15 c r
16 c
17 c
18 c
19 c
20 r c
21 c
22 c
23 c
24 r c
25 c
26 c
27 r c
28 r c
29 r c
You can put this solution on YOUR website! It rained on exactly 11 days during Jane’s holiday trip. On each rainy day it rained either in the morning or in the afternoon but not both. There are
exactly 13 afternoons when it did not rain and exactly 16 mornings when it did not rain. How many days did the trip last?
Taking the other tutor's data as a start
We see right away that there are too many rainy days.
We combine the unassigned PMs with clear AMs with ua AMs with c PMs
We also note
29 c (a+p);11 r (a+p);40 total a+p;20 days needed
There are a total of 13+16=29 am+pm clear
there are 11 am/pm with rain
for a total of 40 am and pm
which is 20 days
13 C-PM
16 C-AM
11 (R-AM +R-PM)
AM PM
1 c r
2 c r
3 c r
4 c r
5 c c 1
6 c c 2
7 c c 3
8 c c 4
9 c c 5
10c c 6
11c c 7
12c c 8
13c c 9
14 r c
15 r c
16 r c
17 r c
18 r c
19 r c
20 r c
So now we have 20 days
11 have rain
9 have no rain at all
-----
9 clear AM and clear PM
7 rained AM 4 rained PM
4 clear PM 7 clear AM
9+4=13 clear am
9+7=16 clear pm
we need
13 C-PM;16 C-AM;11 (RM +RA)
29 c (a+p);11 r (a+p);40 total a+p;20 days needed
all ok
