Question

A tank originally contains 100 gal of fresh water. Then water containing .5 Ib of salt water per gallon is poured into the tank at a rate of 2 gal/min, and the mixture is allowed to leave at a same rate.After 10 min the process is stopped, and fresh water is poured into the tank at a rate of 2 gal/min, with the mixture again leaving ar the same rate. Find the amount of salt in the tank at the end of an additional 10 min. The answer in the book is 7.42 Ib. How do you work it out?

Answer 1

To find the amount of salt in the tank at the end of an additional 10 minutes, we need to calculate the initial amount of salt, the amount of salt added in the first 10 minutes, and then determine the amount of salt after an additional 10 minutes.

Step-by-step explanation:

Let's break down the steps to find the amount of salt in the tank at the end of an additional 10 minutes:

1. First, we need to find the initial amount of salt in the tank. Since the tank initially contains 100 gallons of fresh water, there is no salt in it, so the initial amount of salt is 0 pounds.
2. Next, we need to find the amount of salt that is added to the tank during the first 10 minutes. The rate at which water containing 0.5 pounds of salt per gallon is poured into the tank is 2 gallons per minute, so the amount of salt added in 10 minutes is 2 gallons/minute * 0.5 pounds/gallon * 10 minutes = 10 pounds.
3. After 10 minutes, the process is stopped and fresh water is poured into the tank at a rate of 2 gallons per minute. Since the mixture is leaving at the same rate, the amount of salt in the tank remains the same.
4. Finally, we need to find the amount of salt in the tank at the end of an additional 10 minutes. Since no salt is added during this time, the amount of salt in the tank remains the same, which is 10 pounds.

Therefore, the amount of salt in the tank at the end of an additional 10 minutes is 10 pounds.