Question

for their final chemistry project at louisiana university, nodin and peyton dissolve 112 grams of salt in a vat containing 19 liters of water. then they add water at a rate of 3 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 + 3t liters.
how long will nodin and peyton have to wait until the concentration of salt in the solution reaches 2 grams/liter? minutes. (remember the concentration is the amount of salt divided by the volume of water)
show or upload your work below.

Explanation:

Step1: Set up the concentration formula

Concentration \( C=\frac{\text{Amount of salt}}{\text{Volume of water}} \). Given amount of salt \( = 112\) grams and volume of water \( V(t)=19 + 3t\). We want \( C = 2\). So, \(2=\frac{112}{19 + 3t}\).

Step2: Solve the equation for \(t\)

Cross - multiply: \(2(19 + 3t)=112\).
Expand: \(38+6t = 112\).
Subtract 38 from both sides: \(6t=112 - 38\).
\(6t=74\).
Divide both sides by 6: \(t=\frac{74}{6}=\frac{37}{3}\approx12.33\).

Answer:

\(\frac{37}{3}\) minutes.