Question

A tank with a capacity of 1500 gals originally contains 1000 gals of fresh water. The first pipe containing 2 pounds of salt per gallon is entering at a rate of 4 gal/min. The second pipe containing 3 pounds of salt per gallon is entering at a rate of 6 gal/min. The mixture is allowed to flow out of the tank at a rate of 5 gal/min.

A. Find the amount of salt in the tank at any time PRIOR to the instant when the solution begins to overflow.

Answer 1

2166.67 lbs

Explanation:

Originally the tank had = 1000 gals

Capacity = 1500 gal

water needed more for the tank to overflow = 500 gals

In put of water = I pipe 2 lbs of salt per gallon @ 4 gal / min an d

II pipe 3 lbs of salt @ 6 gals /minute

i.e. inflow = 6 gal/minute

Time taken to overflow =
`(500)/(6)` minutes

Inflow of salt per minute = 4(2) +3(6) = 26 lbs/minute

Hence the amount of salt at the time PRIOR to the instant when the solution begins to overflow.

=
`26((500)/(6) )\\=2166.67` lbs