you and a friend sit still on a spinning merry-go-round. The merry-go-round spins 5 times every second, and to a stationary observer, you have a speed of 9m/s. From your frame of reference, what is the speed of your friend?

From your frame of reference, the speed of your friend is zero.

Explanation:

The speed from a frame of reference is the magnitude of the change of the position per unit of time in that frame of reference.

When it is said that, to a stationary observer you have a speed of 9m/s, it means that the observer "measures" tha your position, in a moment, changes 9 m per second.

Since both you and your friend are sit still on the same spinning merry-go-round, neither of you will change positions with respect to the other, meaning that you will perceive that your friend will not move, from your frame of reference. That is, if you are isolated from the rest of the universe, and the merry-go-round continues spining uniformly, you cannot detect any movement of your friend, which means that from your frame of reference, the speed of your friend is zero.

the other person is right, the answer is zero.