Question

Cod Fish World maintains a storage tank for sea water.

The tank has a volume of $20000000$gallons and is supplied from the ocean by a pipe which pumps $80000$ gallons per hour.

Water is pumped back to the ocean at the same rate.

An aquarium holding $300000$ gallons is fed from the storage tank through a pipe which carries $6000$ gallons per hour, and water is pumped back into the storage tank at the same rate.

Ocean water contains approximately $0.14$ kilograms of salt per gallon.

If $Qs$ is the amount of salt in the storage tank and $QA$ is the amount in the aquarium, measured in kilograms, and time is measured in hours, they obey the equations:

• A. $$\begin{gathered} Q_{S\text{'}}=\frac{Q_A}{50}-\frac{43Q_S}{10000}+11200 \\ {Q}_{A\text{'}}=840-\frac{Q_A}{50} \end{gathered}$$
• B. $$\begin{gathered} Q_{S\text{'}}=\frac{Q_A}{50}-\frac{Q_S}{250}+11200 \\ {Q}_{A\text{'}}=\frac{3Q_S}{10000}-\frac{Q_A}{50} \end{gathered}$$
• C. $$\begin{gathered} Q_{S\text{'}}=\frac{Q_A}{50}-\frac{43Q_S}{10000}+0.14 \\ {Q}_{A\text{'}}=\frac{3Q_S}{10000}-\frac{Q_A}{50} \end{gathered}$$
• D. $Q_{S\text{'}}=\frac{Q_A}{50}-\frac{43Q_S}{10000}+11200$

Answer 1

The correct option is B

$$\begin{gathered} Q_{S\text{'}}=\frac{Q_A}{50}-\frac{Q_S}{250}+11200 \\ {Q}_{A\text{'}}=\frac{3Q_S}{10000}-\frac{Q_A}{50} \end{gathered}$$

Explanation for the correct option:

Determining the correct option

The given data ;

The volume of tank $=20000000$gallons

The rate of water supplied from ocean to the tank $=80000$ gallons per hour

Volume of aquarium $=300000$gallons is fed from tank

The rate of water supplied from tank to the aquarium $=6000$ gallons per hour

Amount of salt in ocean water $=0.14$ kilograms of salt per gallon

Therefore,

Now the amount of salt in storage tank in one hour $Qs$ $=80000\times 0.14-$amount of salt transferred to the aquarium

The amount of salt in aquarium in one hour $Q_A=300000\times 0.41+6000Qs$

Hence the correct option is

$$\begin{gathered} Q_{S\text{'}}=\frac{Q_A}{50}-\frac{Q_S}{250}+11200 \\ {Q}_{A\text{'}}=\frac{3Q_S}{10000}-\frac{Q_A}{50} \end{gathered}$$

Hence, option $\left(B\right)$ is the correct option.