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12 September, 09:38

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.

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  1. 12 September, 09:56
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    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.
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