Final answer:
To obtain a 60% antifreeze solution from a 40% solution, 2 liters of the original mixture should be drained and replaced with 100% antifreeze.
Step-by-step explanation:
How to Make a 60% Antifreeze Solution in a Car Radiator
The problem given is that a car radiator currently contains 6 liters of a 40% antifreeze solution. To achieve a 60% antifreeze solution, an amount of the current solution needs to be drained and replaced with 100% antifreeze. Here's a step-by-step guide to calculate how much of the 40% solution should be drained:
- Determine the amount of pure antifreeze in the original solution: $0.40 \times 6 \text{L} = 2.4 \text{L}$.
- Let $x$ be the amount of the solution to be replaced with 100% antifreeze.
- The volume of the new solution after replacement will still be 6 liters since we are draining and replacing.
- The amount of pure antifreeze after replacement will be $2.4 \text{L} - 0.40x \text{L} + x \text{L}$ (since $x$ liters of 100% antifreeze are added).
- We want the new solution to be 60% antifreeze: $\frac{2.4 \text{L} - 0.40x \text{L} + x \text{L}}{6 \text{L}} = 0.60$.
- Solve the equation for $x$: $2.4 \text{L} + 0.60x \text{L} = 3.6 \text{L}$.
- Rearrange and solve for $x$: $0.60x \text{L} = 1.2 \text{L}$; hence, $x = 2 \text{L}$.
- Therefore, 2 liters of the 40% solution should be drained and replaced with 100% antifreeze to achieve the desired 60% solution.
The calculation above assumes that mixing the solutions will not alter the total volume significantly, which is typical for most liquid solutions unless they have significant volume contraction upon mixing.