Seab E.

asked • 02/02/17

need help solving this problem for a class that I'm taking on fractions. Can someone help me?

There is a swimming pool that has the same depth throughout the entire pool. Three poles are placed vertically in the pool. Their bases are on the bottom of the pool and each pole extends above the surface of the water. 3/4 of the first pole is above the surface of the water. 2/5 of the second is above the surface of the water. 4/7 of the third pole is above the surface of the water. The total length of the three poles combined is 360 cm. 
 
Task 1: Draw a diagram of the situation
 
Task 2: How deep is the pool?

Stella D.

Are you kidding me?  If you are an adult, and you are taking a class on fractions, is this what you would want your students to do?  Google the answer?   Mathematical Practice 1 says to persevere in problem solving.  
 
WHAT DID YOU TRY?
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02/10/17

Mark M.

Whoa, Stella, rather harsh, especially from someone who has not provided any other solutions.
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02/10/17

David W.

I thought perhaps Stella typed a comment in the wrong box (understandable for a newbie).
 
However, the comment does show some misguided understanding of the teaching-learning process.  The reference ("Mathematical Practice 1") must be a very archaic, quite mundane, out-of-style procedure.  While I often heard, "Practice Makes Perfect" when taking piano lessons as a kid, I later learned that "Evaluated Practice Makes Perfect."  Then, I realized that learning uses three distinct formats:  (1) concept/precept, (2) example -- both good and bad, (3) experience.
 
Now, we don't have time or money or enough cat-lives to learn everything by experience; it is a very harsh teacher.  So, selecting the correct process (not just the correct answer) is what efficient/effective learning is all about.  Usually, math is taught by principle, example, then practice.  But if any student, regardless of age, can understand the concept and make use of the information, then skipping the rote practice is fully acceptable.  Note:  Whether I already understand a topic or not, I often look it up (e.g., "Google") rather than try to remember it.  Learning how to quickly find useful information is a very valuable skill (Note:  Would you disallow using IBM's Watson?).
 
As a tutor (more of a coach, mentor, etc.), not a teacher (an evaluator), I am not a "Sage on the Stage, but a Guide by your side."  It is more important to help my students achieve their goals than to insist on "what I want my students to do."
 
The WyzAnt Answers Forum helps many students understand problems (although some students simply seek answers in order to get good grades) by providing explanations -- and by allowing tutors and students to connect for potential private tutoring.
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02/10/17

2 Answers By Expert Tutors

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David W. answered • 02/02/17

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Task 1: Draw a diagram of the situation   (this is approximate; the poles are not the same length):
   Pole 1   Pole 2    Pole 3
     ‡
     ‡
     ‡
     ‡ 
     ‡
     ‡                       ‡
     ‡                       ‡
     ‡          ‡           ‡
     ‡          ‡           ‡
  -  -  -  -  -  -  -  -  -  -  -  -     water level
     ‡          ‡           ‡
     ‡          ‡           ‡
     ‡          ‡           ‡
 ===========================  pool bottom


 
Task 2: How deep is the pool?
  Let the Pole lengths be x, y, z.
 
 "The total length of the three poles combined is 360 cm."       means     x+y+z=360    [eq1]
 
  " same depth throughout the entire pool . . . bases are on the bottom of the pool"    means
           (1/4)x = (3/5)y = (3/7)z
 
           35x  =  84y = 60z               [multiply by LCD=140]
            
             x = (60/35)z
             y = (60/84)z
 
         (60/35)z + (60/84)z + z = 360     [plug into eq1]
             240z  +  100z  +  140z   = 50400       [multiply by LCD=140]
                   480z = 50400
                        z = 105
 
Now, Pole 3 (z) is 3/7 under water.  So, (3/7)*105 = 45.
     The pool is 45 cm deep.   [note:  this is very shallow]
 
To check:
      x = (60/35)(105) =  180
      y = (6084)(105) =     75
      z =                          105
                                  -------
                                     360 cm.
     
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Mark M.

Explanatory visual!
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02/02/17

Seab E.

Thanks to Mark and Dave for your efforts! That Stella is quite harsh in her criticism. I'm not a teacher. I'm an instructiona asst. I've been trying at this problem for two weeks and didn't have any results. I'm going back to school to better myself. I love math and kind of stink at word problems. It's funny that she said to 'Google ' the answer. I did and I was led to this website.
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02/14/17

Mark M. answered • 02/02/17

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Did you draw a diagram?
p represents the length of each pole.
2p/5 + 3p/4 + 4p/7 = 360
56p/140 + 105p/140 + 80p/140 = 360   LCD, 140
240p/140 = 360
240p = 50400
p = 210
 
How deep is the pool? 
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David W.

The poles are not the same length.
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02/02/17

Mark M.

David W., I read that now. Thank you for drawing my attention to it.
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02/02/17

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