Question

A large mixing tank currently contains 350 gallons of water, into which 10 pounds of sugar have been mixed. A tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 3 pounds per minute. Find the concentraion (pounds per gallon) of sugar in the tank after 15 minutes. Is that a greater concentration than at the beginning?

Answer 1

Answer

Let t be number of minutes since tap is opened

water is increased by 20 gallons of water per minute.

sugar increase rate of 3 pounds per minute

water :- W(t) = 350 + 10 t

sugar :- S(t) = 10 + 3 t

concentration

C(t) = $\dfrac{S(t)}{W(t)}$

at t = 15 minutes

C(15) = $\dfrac{S(15)}{W(15)}$

C(15) = $\dfrac{10 + 3\times 15 }{350 + 10\times 15}$

C(15) = 0.11

at beginning t = 0 minutes

C(0) = $\dfrac{S(0)}{W(0)}$

C(0) = $\dfrac{10 + 3\times 0}{350 + 10\times 0}$

C(0) = 0.0286

C(15) > C(0)

hence, concentration is increasing as time is passing.