conveyer belt..

We know that the conveyer belt is 15 feet long and that each circle is 1 foot in diameter. The distance between the two centers of the circles is equivalent to the one horizontal distances that the conveyer belt makes when wrapped around both circles. So, all we have to do is take 15 and subtract the distance that the conveyer belt covers on the right and left circles, which is: pi*d= circumference

Distance that conveyer belt covers on the outer edge of the right circle: pi*1/2=pi/2

Since the distance is the same to both circle, we just multiply pi/2*2 to get the total distance, which is pi. Now subtract pi from 15 to get the combined horizontal distance that the convery belt makes. Since we only want one horizontal distance, we do, 15-pi/2.

the point where the straight line is tangent to the circle falls exactly on the half point of both circles.

so let l = straight line distance.

the curved portion has a total length of pi, b/c diameter of half left circle and diameter of half right circle. (pi/2)*2

we know the total length of the belt is 15.

so we can set up the equation like 15 = 2l + pi and solve for l.

(15-pi)/ 2 = l.

Length of belt=15
sum of circumference of 2 half circles=2*(pi*d/2)=pi*d=pi (since d = 1)
hence distance between belts = (15-pi)/2

since, 15-pi covers twice the distance between two centers.