8. A tank contains 500 gal of a salt-water solution containing 0.05 lb of salt p

ID: 3345133 • Letter: 8

Question

8. A tank contains 500 gal of a salt-water solution containing 0.05 lb of salt per gallon

of water. Pure water is poured into the tank and a drain at the bottom of the tank is

adjusted so as to keep the volume of solution in the tank constant. At what rate (gal/min)

should the water be poured into the tank to lower the salt concentration to 0.01 lb/gal of

water in under one hour (i.e., t = 60 minutes)?

9. A tank initially contains 100 gal of a salt-water solution containing 0:05 lb of salt for

each gallon of water. At time zero, pure water is poured into the tank at a rate of 2 gal

per minute. Simultaneously, a drain is opened at the bottom of the tank that allows the

salt-water solution to leave at a rate of 3 gal per minute. What will be the salt content

in the tank when precisely 50 gal of salt solution remain.

10. A murder victim is discovered at midnight at the temperature of the body is recorded

at 31C, and it was discovered that the proportionality constant in Newton's law was

k = ln(5/4). Assume that at midnight the surrounding air temperature A(t) is 0C, and

is falling at a constant rate of 1C per hour. At what time did the victim die? (Set

T(t) = 37 and solve for t { use a computer or calculator for this part.) [Hint: Letting

t = 0 represent midnight will simplify your calculations.]

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