Question

A tank originally contains 100 gallons of fresh water. Then, water containing 0.5 lb of salt per gallon is poured into the tank at a rate of 2 gallons per minute, and the mixture is allowed to leave at the same rate. After 10 minutes, the process is stopped and fresh water is poured in the tank at a rate of 9 gallons per minute, with the mixture again leaving at the same rate. Find the amount of salt in the tank at the end of an additional 10 minutes.

Answer 1

Answer:

The amount of salt in the tank at the end of an additional 10 minutes are 4.38lb.

Explanation:

Situation 1:

Tank with 100 gallons of fresh water

Situation 2:

Tank with 100 gallons of fresh water + water with 0.5lb of salt per gallon

After 10 minutes, as the rate in which the new water is poured is 2 gallons per minute, the result is 20 gallons added (2×10=20) . And taking in account that the water contains 0.5 lb of salt per gallon the amount of salt added is 20×0.5= 10lb of salt.

That amount of salt is now in all the water inside the tank which is 100 gallons+ 20 gallons= 120 gallons. That means that in situation 2 we have 10lb of salt in 120 gallons of water.

That mixture is allowed to leave the tank at a rate of 2 gallons per minute so we will have after 10 minutes: 120 gallons- (2×10) gallons= 100 gallons remaining in the tank. And the amount of salt if we remember that we had 10lb in 120 gallons, now in 100 gallons we will have: (100 gallons × 10lb of salt)/  120 gallons= 8.33 lb of salt.

Situation 3:

Tank with 100 gallons of water with 8.33lb of salt.

After 10 minutes in which fresh water is poured in the tank at a rate of 9 gallons per minute, the result is: 9×10= 90 gallons added to the tank. So now we have 100+90=190 gallons of water in  the tank. That means in situation 3 we have 8.33 lb of salt in 190 gallons of water.

That mixture is leaving the tank at a rate of 9 gallons per minute so we have after 10 minutes: (190- (9×10))= 100 gallons of mixture remaining in the tank.

And the amount of salt if we remember that we had 8.33lb in 190 gallons, now in 100 gallons we will have: (100 gallons × 8.33lb of salt)/  190 gallons= 4.38 lb of salt.