Problem Solving
8. A 100gal container receives 10gal/min of water and 20gal/min of salt solution with a concentration of 2lb of salt/gal. What is the salt content after 5 minutes? What is the salt concentration after 5 minutes? After x minutes?
Solution:
Draw a sketch of the container with arrows showing what goes in with the concentrations.
The salt content, S, is in lb. The salt concentration, C, is in lb/gal. The time is x.
So S = 20 gal/min * 2 lb/gal * 5min = 200 lb.
(Note that I used the units to help me figure that out.)
And C = 200lb/(100gal + 10gal/min*5min + 20gal/min*5min) = 0.8
If time is variable…
C = (20*2*x)/(100+10*x + 20*x)
C = 40x/(100+30x)
