[bonanova]

Alex and Davey are neighbors and avid volleyball players.

Each has built an asphalt volleyball court in his back yard.

A volleyball court has four sides, with lengths 30 feet and 60 feet, that meet at right angles.

A net bisects the court area and the longer sides of each court.

The sides of both courts run precisely North-South or East-West.

Alex's net runs North-South; Davey's net runs East-West.

Both courts are paved with a 3-inch asphalt layer that exactly fills the court.

The courts were paved the same day, by the same contractor,

who charged each man the same price per cubic foot of asphalt.

Which man paid more for his asphalt?

[Guest]

They paid the same amount of money, but Alex paid more in the long run because he will have to face blinding sun in the early morning or late evening. He should have had his court built the other direction.

[Guest]

I see the concept, but did you calculate the difference?

Two possibilities. If a method is used to ensure an exactly flat surface, then both are identical. Assuming the intent is for the contractor to use a conventional level for insuring flatness, then this is altered by a minute amount by the curvature of the earths surface which is slightly different in east west versus north-south direction. Working the calculations, we find that the variation of material would be less than 0.5 cubic inches. Using reasonable estimates of cubic yard cost, this comes to less than half cent per cubic inch: hence difference in cost would be less than .25 cents. Rounding to the nearest penny, we find the price is the same for this scenario also.

Edited May 7, 2011 by thoughtfulfellow

[pdqkemp]

The reason I think thoughtfulfellow is probably onto the right idea is because I know bonanova is always deep into the mathematical intricacies of problems.

I'll go way out on a limb and try this from a "trick question" point of view nonetheless.

I'll say Davey was the man who paid the most money since Alex is a woman whose whole name is Alexandra.

[Guest]

Davey... reason same as thouhgtfulfellow

earth is more spherical east to west than north to south.

Alex net runs north to south so longer end is east west, so she needs more asphalt than Davey

[Aaryan]

The reason I think thoughtfulfellow is probably onto the right idea is because I know bonanova is always deep into the mathematical intricacies of problems.

I'll go way out on a limb and try this from a "trick question" point of view nonetheless.

I'll say Davey was the man who paid the most money since Alex is a woman whose whole name is Alexandra.

However, pdqkmp, as it clearly states:

The courts were paved the same day, by the same contractor,

who charged each man the same price per cubic foot of asphalt.

Edited May 7, 2011 by Aaryan

[Guest]

Davey, for other reasons . . .

To meet the constraints of the puzzle (90 degree corners, lengths exactly 30 and 60, sides exactly N/S or E/W) these courts must be built on the equator. By doing so, Davey's court net is longer than 30 feet by an amount approximately double the amount by which the length of the other court exceeds 60 feet at the center line. In an algebraic approximation, both courts exceed the nomimal 1800 square feet, but the delta for Davey's court is appox 4 times the delta of the other.

Davey, but for different reasons . . .

[bonanova]

Scott from Eagan

Scott finds the intended solution that just assumes the Earth is a sphere.

Although it's slighly oblate, that does not affect the analysis to first order.

He places the courts at the Equator, so Alex and Davey are E-W neighbors,

and finds the bulging of Davey's long sidelines is greater than the bulging

of Alex's short endlines.

thoughtfulfellow

He observes that at reasonable prices, the likely differences in volume of

asphalt for the two courts makes less than one cent difference in cost.

Thus whatever analysis is used to find differences in volume, they likely paid

the same number of dollars and cents.

Pesos, even, or rupees, since it's at the Equator.

[Guest]

can somebody please tell me what the curvature of the earth has to do with making one court bigger? If both courts are made flat, the earths curves have nothing to do with it.

[Guest]

can somebody please tell me what the curvature of the earth has to do with making one court bigger? If both courts are made flat, the earths curves have nothing to do with it.

It doesn't. The courts must bow out on the sides that run N/S in order to follow the meridian (it was stated they run precisely N/S).

[Guest]

Hey, you dont find Rupees on equator. You are 8 to 9 degrees off.

Scott from Eagan

Scott finds the intended solution that just assumes the Earth is a sphere.

Although it's slighly oblate, that does not affect the analysis to first order.

He places the courts at the Equator, so Alex and Davey are E-W neighbors,

and finds the bulging of Davey's long sidelines is greater than the bulging

of Alex's short endlines.

thoughtfulfellow

He observes that at reasonable prices, the likely differences in volume of

asphalt for the two courts makes less than one cent difference in cost.

Thus whatever analysis is used to find differences in volume, they likely paid

the same number of dollars and cents.

Pesos, even, or rupees, since it's at the Equator.