Problem is as shown in the picture.
The answer is meant to be a 4.59mm.
The Attempt at a Solution
Force (tau) acting on plate from both fluids is equal, as is velocity (du).
mu1 (du/dy1) = mu2 (du/dy2)
mu1/dy1 = mu2/dy2
(mu2/mu1) *y1 = y2
y1 + y2 + plate thickness = width
y1 + y2 + 0.7937 = 12.7 mm
By substituting in mu2/mu1 *y1 = y2 I obtain the answer y1 = 3.31 mm.
Any help is much appreciated