# A tank with a capacity of 100 gallons initially contains 50 gallons of water with 10 pounds of salt in solution. fresh water enters at a rate of 2 gallons per minute and a well-stirred mixture is pumped out at the rate of 1 gallon per minute. compute the amount of salt (in pounds) in the tank at the first moment when the tank is filled.

2 months ago

## Solution 1

Guest #9861
2 months ago
Let be the amount of salt (in pounds) in the tank at time . We're given that.

The rate at which the amount of salt in the tank changes is given by the ODE

Given that , we find that

so that the amount of salt in the tank is described by

The tank will be filled when , or after minutes. At this time, the amount of salt in the tank is

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