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Question

Directions: Show all work, and answer each question that is asked. Explanations should be given in complete sentences. All graphs should be drawn accurately on this sheet, and be fully labeled.

1. The Joker is preparing his next laugh for Batman using a water processing plant on the outskirts of Gotham. A large mixing tank currently contains 105 gallons of water into which 5 pounds of powdered acid have been mixed. A tap will open pouring 15 gallons per minute of water into the tank at the same time acid is poured into the tank at a rate of 1 pound per minute. Find the concentration (pounds per gallon) of acid in the tank after 15 minutes. Is that a greater concentration than at the beginning?

Explanation / Answer

The initial concentration of acid in the tank is 5lb/105 gallons = 1/21 lb/gallon.

After 15 minutes, the quantity of water in the tank is 105 +15*15 = 105 +225 = 330 gallons and the quantity of acid is 5+ 15 = 20lbs. Thus, the concentration of acid in the tank after 15 minutes is 20/330 = 2/33 lb/gallon.

Since 2/33 > 1/21, hence the concentration of acid in the tank after 15 minutes is a greater concentration than at the beginning.

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