[Prof. Templeton]

There was once a very forgetful landscape contractor who was constantly “misrembering” the detailed instructions of his employers. He was always forgetting essential parts of what the customer had intended and instead would substitute his own without realizing it. How he stayed in business as long as he did is a mystery. Here is one example of his forgetfulness:

The customer had two stone walls, each a square, one inside the other and a path that ran between. He wanted an irrigation pipe installed in the ground in the area inside the two walls.

"I've already measured everything. If you dig a trench and lay the water pipe in a circle it will be inscribed inside the outer wall and the inner wall will be inscribed in the circle. Do you understand what I'm saying?"

“No problem”, replied the contractor. “I’ll get to work as soon as I can get my equipment back here”.

When the contractor returned he proceeded to dig a square trench between and equidistant to the two walls and installed the pipe.

The customer came out to check on the installation. "That's not what I asked for. You have dug a square and not a circle", he said. "I suppose it doesn't really matter as long as things get watered. Since we agreed that I would pay you per foot of pipe installed, the bill will have to be changed."

"Ummm...Oh, of course", replied the contractor.

What was the percentage of change in the bill?

[Glycereine]

(2+sqroot(2))/pi

Or 109%

[Guest]

I think the customer paid about 8% more than he originally should have if the contractor would have made a circle.

[Guest]

i think he lost money... it was a decrease of 9% going to a square...

[Guest]

agreed 8.67% moreish

[Guest]

i think he lost money... it was a decrease of 9% going to a square...

I did it saying he had a 100ftx100ft square as the bigger one. Draw a circle around inside it. Draw the biggest square you can inside the circle, which is about 70.71ftx70.71. Now to center the square the contractor made, you take 100-70.71=29.29, half of that is 14.64. Add 14.64 to the 70.71 and you get about 85.35x85.35.

The circle was 314 ft around worth of pipe.

The square the contractor made was about 341.4

Thats how I got about 8% overpayment from what the customer originally wanted.

Hav'nt done a problem like that in years so my math may be off, if anyone wants to check it.

[Guest]

There was once a very forgetful landscape contractor who was constantly “misrembering” the detailed instructions of his employers. He was always forgetting essential parts of what the customer had intended and instead would substitute his own without realizing it. How he stayed in business as long as he did is a mystery. Here is one example of his forgetfulness:

The customer had two stone walls, each a square, one inside the other and a path that ran between. He wanted an irrigation pipe installed in the ground in the area inside the two walls.

"I've already measured everything. If you dig a trench and lay the water pipe in a circle it will be inscribed inside the outer wall and the inner wall will be inscribed in the circle. Do you understand what I'm saying?"

“No problem”, replied the contractor. “I’ll get to work as soon as I can get my equipment back here”.

When the contractor returned he proceeded to dig a square trench between and equidistant to the two walls and installed the pipe.

The customer came out to check on the installation. "That's not what I asked for. You have dug a square and not a circle", he said. "I suppose it doesn't really matter as long as things get watered. Since we agreed that I would pay you per foot of pipe installed, the bill will have to be changed."

"Ummm...Oh, of course", replied the contractor.

What was the percentage of change in the bill?

about 8.6%

[Guest]

Amarnath_Caterpillar

I appreciate the way you put the question.

Lets assume the inner square of side 1 m.

By calculations the circle inscribed between the two squares is of diameter = root2 m.

The outer square if of side = root2 m.

Then the perimeter of the circle if dug between the squares = pi*root2=4.44 m

The perimeter of Square dug between the two walls = 4* (1+ (root2-1)/2)= 4.828 m

Percentage increase in the price = (4.828-4.44)*100/4.44= Square pipe line is 8.74% more price than the circular pipe line.

[Guest]

i just use good ole algebra

big square has side 2r,

circle has radius r,

small square has diagonal 2r so side squreroot(2)r,

square in between has side (2r+squareroot(2)r)/2

so (4(2r+squareroot(2)r)/2)/2pi®=(2+squareroot(2))/pi as dynamite said

[Guest]

There doesn't seem any need for me to put my spoke in, as so many have already solved this one.

I did this by sketching a diagram, checking the exact wording and then doing the maths.

I rather like the elegant simplicity of the ratio between the two distances, i.e 2+sqrt2 : Pi

Donjar

[Guest]

;)the % change in the bill is 8.67%

There was once a very forgetful landscape contractor who was constantly “misrembering” the detailed instructions of his employers. He was always forgetting essential parts of what the customer had intended and instead would substitute his own without realizing it. How he stayed in business as long as he did is a mystery. Here is one example of his forgetfulness:

The customer had two stone walls, each a square, one inside the other and a path that ran between. He wanted an irrigation pipe installed in the ground in the area inside the two walls.

"I've already measured everything. If you dig a trench and lay the water pipe in a circle it will be inscribed inside the outer wall and the inner wall will be inscribed in the circle. Do you understand what I'm saying?"

“No problem”, replied the contractor. “I’ll get to work as soon as I can get my equipment back here”.

When the contractor returned he proceeded to dig a square trench between and equidistant to the two walls and installed the pipe.

The customer came out to check on the installation. "That's not what I asked for. You have dug a square and not a circle", he said. "I suppose it doesn't really matter as long as things get watered. Since we agreed that I would pay you per foot of pipe installed, the bill will have to be changed."

"Ummm...Oh, of course", replied the contractor.

What was the percentage of change in the bill?

8.67%

[Guest]

Approx 8.67% Increase

Forgetful_Landscaper_Puzzle_Riddle.bmp

[Guest]

The bill did not get changed because the pipe that is going to be laid down is the same. The only change to the project was the trench that was dug.

Maybe...

[Guest]

It appears this has already been answered, but I wanted to test my old math skills so I have not yet read the spoilers.

so basically, the smaller square would need to obviously be smaller than the big one with a particular ratio to allow it to be inscribed by the circle. I also am assuming that the two squares have parallel sides since there is a walking track between. If that is the case, the inner square would be equal to half the side length of the large square (x) times the square root of two, minus itself (x), or approximately .414(x). This would make the circumference (pi)*0.828x.

The square path would then be 8*.414/sqrt(2). Setting x =1, The round path would be approximately 11.05% longer than the square path, thus the price would increase by that much.

[Guest]

You are given four shapes and no exact distances. Only thing you can use to solve are formulas, or the math behind these formulas.

The four shapes are Outer square (OS), Inner Square (IS), The Circle Trench (CT), and the Square Trench (ST)

Based on the layout depicted in the questions the following are given.

The Diameter of CT = d

Thus the circumference of CT = Πd = 3.14159d

The side of OS = d ( as the circle is inscribed inside the outer wall)

The diagonal of IS = d (as inner wall will be inscribed in the circle)

Thus the side of IS= d/1.41 = .7092199d

The Difference in the two sides divided by 2 will be the extra distance added to the IC to establish the length of TC’s side.

The side of TC = (d - .7092199d)/2+.7092199d = .290780141844d/2+ +.7092199d = .854609970922 d

The perimeter of TC = .854609970922 d * 4 = 3.418439883688 d

The change in price will = perimeter of TC / circumference of CT- 1 = 3.418439883688d/ 3.14159d -1 = 1.08669- 1= .08669 = 8.67% increase

landscaper.bmp

[Guest]

oh, I see what I did, I found the perimeter of the inner square, not the one between the big and little.