Fluid flow & mixture

[Ether]

Let Vdot be the volume flow rate in gallons per minute (gpm) in each hose.

Let B(t) be the amount (in gallons) of Fluid B in Bucket1 at time t minutes.

At any given time t, Fluid B is entering Bucket 1 at the rate Vdot gpm, and is draining out of Bucket 1 at the rate Vdot*B(t)/5 (assuming perfect and instantaneous mixing).

Thus we have the differential equation dB(t)/dt = Vdot(1-B(t)/5)

See attached screenshot "buckets.png" for the DE solution in Maxima*. Assuming instantaneous and perfect mixing, the answer is independent of flow rate Vdot. So pick Vdot=5 gpm and t=1 minute to calculate the solution

3.16 gallons (63.2%) of Fluid B in Bucket1.


*Or you could solve the DE manually by separating the variables and integrating. See attached screenshot "separate_vars.png".