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Title
Water Stop

Problem Statement
The rectangular field pictured has unknown dimensions. Tom and Paul are both at point A. Tom walks straight from A to C. To get a drink, Paul walks from A to B, then from B to C. How far does Paul walk if he travels 40 yards farther than Tom? What are the dimensions of the field?


Plans to Solve/Investigate the Problem

I plan to set up a system of equations to solve this problem.

 

Investigation/Exploration of the Problem

I first set up two equations. The first one is based on the distanced walked by Tom and Paul. The second equation is based on the Pythagorean theorem.

 

AB + BC = AC + 40

(AB)² + (BC)² =  (AC)²

 

I realized that I had 2 equations with 3 variables and this would be difficult to solve. Next I began to think of Pythagorean triples I knew to see if they would work. After trying a few, I took 3,4, and 5 and began listing the triples I would get by multiplying by 2,3,4,5…..until I reached a solution.

 

3,4,5

6,8,10

9,12,15

12,16,20

15,20,25

18,24,30

21,28,35

24,32,40

27,36,45

30,40,50

33,44,55

36,48,60

39,52,65

42,56,70

45,60,75

48,64,80

51,68,85

54,72,90

57,76,95

 

 The solution I found was 60, 80 and 100.

 

Author & Contact
Insert name and contact information.
Dottie Mitcham


 

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