What is the Angular Velocity of Gear 5 in a Differential Gear System?

[Jonski]

Homework Statement

Gear 2 in the figure below is driven at a speed of 80 rpm in the CCW direction viewed from the right end. Gear 4 meshes with a fixed ring gear (gear 7) and with gear 5. Find the angular velocity of gear 5. N2= 16 T, N3= 32 T, N4= 30 T, N5= 22 T and N7= 77 T.

Homework Equations

w1/w2 = -N2/N1
w = angular velocity
N = number of teeth

(wsun - wcarrier)/(wring - wcarrier) = -Nring/Nsun

The Attempt at a Solution

wcarrier = 80 rpm
wring = 0 as its fixed
wsun = w5

w5 -wc = 77/22 * wc
w5 - 80 = 3.5*80
w5 = 360rpm

This is incorrect however, and I think it is because w3 has an effect on w4 which in turn effects w5.
w3 = -40 = w4;
However I'm not sure how to connect these two values, any help would be much appreciated

 

[Bystander]

If you're told, "This is a differential," can you re-examine the question productively?