Question

A large tank is partially filled with a solution. The tank has a faucet that allows solution to enter the tank at a rate of 16 3/4 liters per minute. The tank also has a drain that allows solution to leave the tank at a rate of 19 4/5 liters per minute. (a) What expression represents the change in volume of solution in the tank in 1 minute? (b) Simplify and give your answer as a simplified mixed number. (c) What is the change in volume of the solution after 10 minutes? Show necessary work. Give your answer as a simplified mixed number.

Answer 1

The change in volume per minute and the total change in the volume of the solution after 10 minutes will be $- 3 \frac {1}{20} \: litres$ and $- 30 \frac {1}{2} \: litres$ respectively.

• Entry rate = $16 \frac{3}{4}$ per minute

• Discharge rate = $19 \frac{4}{5}$ per minute

Change in the volume of solution in the tank per minute can be calculated thus :

• Change in volume = (Entry rate - Discharge rate) × time

• $16 \frac{3}{4} - 19 \frac{4}{5} = \frac{67}{4} - \frac{99}{5} = \frac{(335 - 396)}{20} = \frac{-61}{20} = - 3\frac{1}{20} \: litres \: per \: minute$

The total change in the volume of solution in the tank after 10 minutes can be calculated thus :

• Change in volume per minute × time

• $- \frac{61}{20} \times 10 = - \frac{610}{20} = - 30 \frac {1}{2} \: litres$

Therefore, the solution in the tank decreases by $30 \frac {1}{2} \: litres$ after 10 minutes

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