Question

A carousel has eight evenly spaced seats shaped like animals. During each ride, the carousel makes between 8 and 9 clockwise revolutions. At the end of one ride, the carousel stops so that the lion is in the position where the zebra was when the ride started. Through how many degrees did the carousel rotate on this ride

Answer 1

-2970, -3320

Explanation:

The carousel makes between 8 and 9 clockwise revolutions

the position of the lion rotated to that of the zebra is two steps

now,

1 revolution = 360 degrees accomplished in 8 steps

1 step = 360/8 = 45 deg

=> position of lion rotated to zebra = 2 × 45 = 90 deg

if 1 revolution = 360 accomplished in 9 steps

then

1 step = 360/9 = 40 deg

=> position of lion rotated to zebra = 2 × 40 = 80 deg

since the rotation is in clockwise direction, a negative sign is required

FOR 8 Revolutions

in total the carousel rotates

-[8(360) + 90] degrees

= -2970 degrees

FOR 9 revolution

in total the carousel rotates

-[9(360) + 80] degrees

= -3320 degrees

Answer 2

2931 + 51.4n/7 degrees where n is the number of animal from the lion to the zebra in the clockwise direction.

Explanation:

We don't have details on the positions of the lion and the zebra prior to revolution but suppose the zebra is n animal away from the lion where n could be in the range of 0 to 6 in the clockwise direction. If n = 0, the zebra is next to the lion in line, and if n = 6, the zebra is right behind the lion.

In angular term, since all 8 animals are evenly spaced, there are 7 space in between them, each of them would span an angle of 360/7 degrees

Then the angular distance between the zebra and the lion is (n+1)360/7 degrees

If the carousel makes between 8 and 9 revolutions then the total angular distance is 8*360 + (n+1)360/7 = 2931 + 51.4n/7 degrees