As shown in the figure above, a thin conveyor belt 15 feet long is

It is always better to include the picture rather than just reference the picture. You're more likely to get responses by putting in the actual question.



As shown in the figure above, a thin coveyor 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) [m]\frac{15-∏}{2}

b) [m]\frac{5∏}{4}

c) 15 - 2∏

d) 15 - ∏

e) 2∏

A is correct because you have 15 total feet around the belt. There are 2 wheels, but instead of subtracting the circumference of both wheels, we only have to do the circumference of 1 wheel because the belt is only touching 1/2 of each wheel. The diameter is 1 foot, so in terms of circumference, that is ∏ * diameter or ∏. See the picture below.

The red represents what has not been determined by the circumference of the wheel. The length of each red segment is the same length as the distance between the centers of the wheel. Because these 2 red segments are part of the belt, we know it's length is 15 feet long, minus the portion we just figured for around each half of the wheel, or 15 - ∏, but this is the length for both of them, and the distance between the center of the wheels is the same as the length of only one (1) of them, so we need to divide by 2. That give us a) for the answer.