Problem 6
A mixture of water, sand and tiny plastic bits is fed into a processing unit continuously at a flow-rate of
7.0 kg/min. In this mixture, the solid content is 72% sand and 28% plastic (by mass). The processing
unit outputs pure sand and waste. The waste contains water (63% by mass), plastic (35% by mass), and
sand (2%). Determine the percentages of water, sand and plastic in the original mixture. How much
pure sand does the processing unit output in 3 hours?
Hints:
1) Assume a uniform, steady rate-flow process.
2) Let x denote the percentage of water in the original mixture. Then the solid content (sand and
plastic) in the original mixture is (100% - x)7.0 kg/min.
3) To solve this problem, an instructor developed a system of five linearly independent equations.
The instructor wrote more than five equations, but needed to choose five linearly independent
equations to solve for the unknowns. Do you have to write a system of 5 equations? No. There
are different approaches. \"To use the given hint or not to use\" is up to you. You can have a
system of 3 equations to solve, and then do other calculations. In any case, please present your
work according the Mass Balance Problem Solving Procedure (Algorithm).
