Pulley problem: Does the third pulley move up or down?

[21joanna12]

Homework Statement

) The pulley system in Figure 1.b consists of two pulleys of radii a and b rigidly fixed
together, but free to rotate about a common horizontal axis. The weight W hangs
from the axle of a freely suspended pulley P, which can rotate about its axle. If
section A of a rough rope is pulled down with velocity V :
(i) Explain which way W will move.
(ii) With what speed will it move?
THE IMAGE IS IN QUESTION 3 HERE: http://www.physics.ox.ac.uk/olympiad/Downloads/PastPapers/BPhO_Round_1_2013_prt_1.pdf

Homework Equations

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The Attempt at a Solution

The answer is that the weight will move up because rope B moves down with velocity (b/a)V and D moves up with velocity V, so the centre of the weight rises with speed V(a-b)/2a

I really can't see why the mass would move up. Surely the same amount of string is fed through to each side of the pulley so it should not move?

Thank you in advance!

 

[gneill]

Imagine that the rope does not slip on the pulleys. If the top pulleys rotate through some small angle θ, how much will a point on segment D rise? How much will a point on segment B drop?