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
U
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