QuestionFor their final chemistry project at Indiana University, Bastián and Isaiah dissolve 161 grams of salt in a vat containing 19 liters of water. Then they add water at a rate of 4 liters of water per minute until the concentration reaches 2 grams/liter.
The volume of water after $t$ minutes is given by $V(t)=$ $19+4 t$ $\square$ liters. $\qquad$ How long will Bastián and Isaiah have to wait until the concentration of salt in the solution reaches 2 grams/liter? $\square$ minutes. (Remember the concentration is the amount of salt divided by the volume of water)

Studdy Solution
Solve for the time when the concentration reaches 2 grams per liter.
Multiply both sides by $19 + 4t$ to clear the fraction: $$161 = 2(19 + 4t)$$
Expand the right side: $$161 = 38 + 8t$$
Subtract 38 from both sides to isolate the term with $t$: $$161 - 38 = 8t$$ $$123 = 8t$$
Divide both sides by 8 to solve for $t$: $$t = \frac{123}{8}$$ $$t = 15.375$$
Since time is typically measured in whole minutes, Bastián and Isaiah will have to wait approximately $\boxed{15.375}$ minutes for the concentration to reach 2 grams per liter.