A 50 L tank initailly contains 10 L of fresh water, At t=0, a brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 L/min, while the well-stirred mixture leaves the tank at the rate of 2 L/min. Then the amount of time required for overflow to occur in

Options

A. 30 min
B. 20 min
C. 10 min
D. 40 min

Answer

B

Explanation

Here, `a=0, b=1, e=4, f=2` and `V_(0)-10`.
The volume of brine in the tank at any time t is given as
`V_(0)+et-ft=10+2t`
We require t when `10+2t=50`. Hence, t=20 min.