Part 1 of 2
For their final chemistry project at Delaware University, Malachi and Thandiwe dissolve 197 grams of salt in a vat containing 20 titers of water. Then they add water at a rate of 4 liters of water per minute until the concentration reaches 7 grams/liter.
The volume of water after $t$ minutes is given by $V(t)=20+4 t$ liters.
Part 2 of 2
How long will Malachi and Thandiwe have to wait until the concentration of salt in the solution reaches 7 grams/liter? minutes. (Remember the concentration is the amount of salt divided by the volume of water)
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Final Answer: Malachi and Thandiwe have to wait approximately \(\boxed{2.04}\) minutes until the concentration of salt in the solution reaches 7 grams/liter.
Step 1 :Given that Malachi and Thandiwe dissolve 197 grams of salt in a vat containing 20 liters of water. Then they add water at a rate of 4 liters of water per minute until the concentration reaches 7 grams/liter.
Step 2 :The volume of water after \(t\) minutes is given by \(V(t)=20+4 t\) liters.
Step 3 :We need to find how long will Malachi and Thandiwe have to wait until the concentration of salt in the solution reaches 7 grams/liter. The concentration is the amount of salt divided by the volume of water.
Step 4 :To solve for \(t\), we can first multiply both sides of the equation by \((20 + 4t)\) to get rid of the denominator on the left side. This gives us \(197 = 7 * (20 + 4t)\).
Step 5 :Then we can distribute the 7 on the right side to get \(197 = 140 + 28t\).
Step 6 :Subtracting 140 from both sides gives us \(57 = 28t\).
Step 7 :Finally, we can divide both sides by 28 to solve for \(t\).
Step 8 :Doing the calculation gives us \(t = 2.0357142857142856\).
Step 9 :Final Answer: Malachi and Thandiwe have to wait approximately \(\boxed{2.04}\) minutes until the concentration of salt in the solution reaches 7 grams/liter.