As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels...

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GMAT Prep

As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?

A. (15−π)/2

B. (5π)/4

C. 15−2π

D. 15−π

E. 2π

OA A

[Jay@ManhattanReview]

GMAT Prep

Conveyer Belt.jpg

As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?

A. (15−π)/2

B. (5π)/4

C. 15−2π

D. 15−π

E. 2π

OA A

From the given information, we know that length of the belt
= 2*(1/2 of the circumference of each wheel) + 2*(Distance between the centers of the two wheels)
=> 15 = Circumference of the wheel + 2D
15 = 2πr + 2D
15 = π*1 + 2D

D = (15 – π)/2

The correct answer: A

Hope this helps!

-Jay
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[Scott@TargetTestPrep]

GMAT Prep

Conveyer Belt.jpg

As shown in the figure above, a thin conveyor belt 15 feet long is drawn tightly around two circular wheels each 1 foot in diameter. What is the distance, in feet, between the centers of the two wheels?

A. (15−π)/2

B. (5π)/4

C. 15−2π

D. 15−π

E. 2π

OA A

We should first note that the conveyor belt can be decomposed into two semicircular pieces, each of which has radius 0.5 meters, and two straight pieces, each of which has a length equal to the length between the centers of the two wheels.

Since each wheel has a radius of 0.5 meters, we know that the circumference of each wheel is 2 x π x 0.5 = π meters. Since the belt goes around half of each circle, a length of π/2 meters of the belt goes around each circle. However, since there are two circles, a length of 2 x π/2 = π meters of the belt goes around the two semicircles.

The entire belt is 15 meters long, so the two straight pieces of the belt have a combined measure of (15 - π), which means the distance between the centers of the circles is (15 - π)/2.

Answer: A