| Solution
to prior Problem of the Week
For the week of November 4, 2002
The Problem
Hurricanes can cause
storm surge—when the water of the storm rises much higher than usual.
Storm surge is very dangerous and can sweep away homes that are built
right along the beach. To prevent this, many people living near water
build their houses on stilts. For example, in the town of Palm Nut Beach,
the homes are the water are built on stilts that are constructed so that
¼ of the pole is stuck in the solid ground. In 2000, Andy, a homeowner
in Palm Nut Beach, noticed that storm surge covered 1/3 of the stilt that
was sticking out of the ground, leaving 5 feet dry. After the storm, the
waters receded back to normal. Then, in 2002, Andy noticed that the storm
surge covered ¾ of the stilt that was sticking out of the ground.
a) How many feet high
did the storm surge in 2002?
b) How many feet of Andy’s stilt was left dry in 2002?
Challenge:
Bob, another homeowner, used stilts of the same length as Andy but installed
them slightly differently. He constructed his house so that 40% of each
stilt was stuck in the ground. During the storm surge of 2002, did his
house get washed away because the storm was higher than the stilt? Please
explain your answer.
Highlighted Solutions
Student's Name: Victoria
Answer(or question to Mentor): Solution: a) 5.625 feet b) 1.875 Rationale:
1/4 of the stilt is under the ground. So 3/4 is above ground. 1/3 of what
was out of ground was covered. And 5 feet was dry. I did 5 divided by
2 and got 2.5. Then I added 2.5 to 5 to get 7.5 as the stilt sticking
out of the water. So in 2002 the stilt sticking out of the ground was
7.5 and 1/4 of it was dry or 1.875 feet. 3/4 was wet. 1.875 times 3 =
5.625 feet.
Student's Name: Kevin
Answer(or question to Mentor): Problem Solution: A. 5.625 feet B. 1.875
feet Problem Rationale: A. If ¼ of the pole was buried, then ¾
of the pole was exposed. Of the exposed pole, 1/3 was covered in 2000
by the storm surge, leaving 5 feet dry. If 5 feet=2/3 of the exposed pole,
then 1/3 of the exposed pole = 2.5 feet. So 5 feet + 2.5 feet = 7.5 feet
of exposed pole. To find out how much of the exposed pole was covered
in 2002, I multiplied the amount of the exposed pole, 7.5 feet, by ¾
(75%), which equaled 5.625 feet. B. Since the exposed pole = 7.5 feet,
I subtracted the covered amount, 5.625 feet, from the total exposed amount
of 7.5 feet, which equaled 1.875 feet. Challenge Solution: No, his house
was not washed away. Challenge Rationale: Since Andy and Bob have the
same size poles, I can use the information about Andy’s pole to figure
out the original size of both poles. The exposed part of Andy’s pole is
¾ of the total length. I know that ¾ of the total length
is 7.5 feet. If total length is “X”, then ¾ * X = 7.5 feet. If
I divide 7.5 feet by ¾, this equals 10 feet, the total original
size of the pole. Since the total length of Bob’s pole was 10 feet and
40%, or 4 feet, was buried underground, then 6 feet was left exposed.
Since the storm surge in 2002 was only 5.625 feet, I know that there was
0.485 feet left until the poles were completely covered by subtracting
5.625 feet from the 6 feet of the exposed pole.
Student's Name: Katie
Answer(or question to Mentor): Ok Noemi, I think I have it this time.
My soulution for the problem is if the storm covered 1/3 of the pole and
leaving 5 feet dry in 2000 then that means 2/3 are left dry. 2 ½
times 2 equals 5 so you add 2 ½ to 5 and get 7 ½ feet for
the pole sticking out of ground in 2000. All the numbers are in feet so
not to worry. Now if the storm surge covered ¾ feet of the pole
in 2002 then ¼ was dry. So you multiply 7 ½ feet by ¾
feet in which you convert 7 ½ feet into 15/2 feet. It turns out
to be 45/8 or 5 5/8 feet. So the storm surge rose 5 5/8 feet. Now for
the second part of the question. Since the storm surge was 5 5/8 high
then 1 7/8 feet was left dry. I did thid by subtracting 7 ½ by
5 5/8.
Student's Name: Mattie
Answer(or question to Mentor): I’m still not sure I understand how to
do this problem. I did what you said thought I drew a diagram. I’m pretty
sure this is incorrect but this is what I did and if I did miss it again,
I want to figure out what I am doing wrong. PROBLEM SOLUTION: A. The storm
surged 5.625 feet in 2002. B. There was 1.875 feet of the pole left dry
in 2002. RATIONALE: A. Like you suggested I drew a diagram of the pole
for 2000. Since 1/3 was covered in water I divided it into 3 sections
to make it easier for me to work with. The 1/3 of the pole that was covered
in water I shaded in. Beside the part left blank I wrote 2/3=5 feet, again
just to make it easier for me. Since 2/3=5 feet I divided 5 feet into
2 parts and found that each of the 2 parts that was dry was 2.5 feet.
And since each of those was 2.5 feet I knew the 1/3 of the pole that was
underground had to be 2.5 also. Since there were 3 “parts” of the pole,
each 2.5 feet, I multiplied 2.5 times 3 and found that the entire pole
was 7.5 feet.
B. Since it was the
same pole in 2002 as it was in 2000, I knew that the pole was 7.5 feet
high. I also knew that ¾ was covered in water, so obviously ¼
was dry. This time I divided the pole I drew into 4 parts, since ¼
of the pole was dry. Again I shaded the ¾ that was in water and
left the ¼ that was dry blank. Since I knew the pole was 7.5 feet
I divided it by 4, since there were 4 “sections,” and found that each
“section” was 1.875 feet. Since only ¼ of the pole was covered
in water, and ¼ of the pole was 1.875 feet, then 1.875 feet of
the pole was left dry. I couldnt send it all at 1 time so i sent it in
2 parts agian. Thanks for helping me and explaining what i should have
done differently, it helped. Talk to you later, Mattie
Student's Name: Alex
Answer(or question to Mentor): Problem Solution: The storm surged 5.6
feet in 2002 also in the same year 1.9 feet of stilt was left dry. Problem
Rationale: I got these answers by first finding out how many feet of stilt
was left out of the ground. I did this by dividing 5 feet, which is 2/3
of the stilt, by 2 and getting a solution of 2.5 feet a 1/3. I then added
2.5 to 5 and got a total number of 7.5 . Then to figure out how high the
storm surged I multiplied 7.5 by .75, which is 3/4, and getting a total
of 5.6 feet. To find the answer to how many feet of the stilt were dry
I subtracted 7.5 by 5.6 to get the solution of 1.9 .
Challenge:
Student's Name: Eric
Answer(or question to Mentor): Challenge Solution: No, but just barely.
The waters surged 9 5/8 of the pole. Challenge rationale: Because the
pole is 10 feet long and 40% of the pole is underground, I multiply .4(10)
to find how much is undergrouund. 4 feet is underground,leaving six feet
aboveground. From the information in the *problem* I found that the storm
surged 5 and 5/8 feet. There is six feet above ground, it surged 5 and
5/8 feet, six feet is higher than 5 5/8 feet. Therefore, the house just
barely stayed above water. Or... 4 feet undergorund + the water aboveground(5
5/8)= 9 5/8. 9 5/8 is less than ten sooo... The house survived. This problem
sounds too fishy... I think that it is too easy to be a challenge problem.
I think I did something wrong, but I don't know what. Please respond soon
so I can know what I did wrong, if I did do something wrong.
Student's Name: Katie
Answer(or question to Mentor):CHALLENGE: If Bob used the same length poles
but it went 40%feet into the ground then you would have to figure out
how long the poles are with all the information you already have. If ¼
feet of the pole is in the ground then all you have to do is add 2 ½
to it because the pole above ground equals 7 ½ already by adding
2 ½ together three times. That will give you a ten foot pole. Sorry
if it is a bit confusing because it is kind of hard to explain. So anyways,
since the pole is 10 feet tall the 40% into 10 equals 4. Add 4 feet to
5 5/8 dry because that's how much the storm surged. You come out with
9 5/8 feet leaving 3/8 feet left so no, Bob's house was not washed away,
but it did come close. I hope I did much better this time. If I confused
you I am so sorry. Please let me know soon. Thanks, bye, KT
Student's Name: Victoria
Answer(or question to Mentor):Challenge Solution: No Bob’s house was not
washed away. Rationale: the total stilt was 10 feet. 40% was in the ground
(4 feet) so 60% was out of the ground. 60 % of 10 feet is 6 feet. The
water rose 5.625 feet and that is smaller than 6 feet. So the house was
not washed away.
Student's Name: Alex
Answer(or question to Mentor): Challenge: The house didn't get washed
away because 0.4 feet of the stilt were left out of the ground Rationale:
I found out that the stilt is 10 feet in all and then 40% of 10 feet is
4 and subtracted that from 10 and got 6 the water raised 5.6 feet and
i subtracted that from 6 and got .4
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