Low-grade phosphate rock can be upgraded by flotation processing. In this process the low-grade rock is grounded into a powder and suspended as a water slurry. The addition of small amounts of oil and other surface active agents causes the phosphate to adhere to air bubbles. By frothing the slurry with air, a phosphate rich foam floats off the top of a froth flotation unit, while the heavier waste rock leaves at the bottom. A two stage flotation unit designed to produce a 20% P₂O₅ concentrate from a 5% low grade rock is illustrated below. (Note: the phosphate content of the samples is reported as P₂O₅). Laboratory data for the process gave the following stream analysis: Stream Wt%  P₂O₅ on a Dry Basis

Feed F             5

Waste W         1

Recycle R        10

Stream Q         12

Product P        20

All the streams consist of a slurry of approximately 30% solids. The weight of the frothing agents is negligible compared to the weight of the ore processed.

(a) Calculate the percentage of the phosphate in the feed material that is recovered as the product.

(b) Calculate the flow rates of all the stream if 100 metric tones/hr of feed enters the process

(c) How much water leaves with the waste-rich stream per hour?