Layered Fluids Problem:

A lock gate is to be strengthened by installing three matching girders horizontally on the gate. The water is five meters deep on both sides of the gate while on the right side of the gate, a layer of oil $(SG=0\mathrm{.}85)$ that is $1\mathrm{.}2$ metersthick, floats on top of the water due to a recent oil spill.

Calculate the load on each girder $($per unit length in meters$)$ if they are designed to carry equal magnitudes of load. Also, calculate the locations of the girders $(d_1,d_2,$ and $d_3)$ from the bottom so that the condition stated holds true. Note that the gate is mounted on top of roller supports and water does not seep through this support.