The radiator in a car is filled with a solution of 70 per cent antifreeze and 30 per cent water. The manufacturer of the antifreeze suggests that for summer driving, optimal cooling of the engine is obtained with only 50 per cent antifreeze. If the capacity of the raditor is 4 liters, how much coolant (in liters) must be drained and replaced with pure water to reduce the antifreeze concentration to 50 per cent?

Question

The radiator in a car is filled with a solution of 70 per cent antifreeze and 30 per cent water. The manufacturer of the antifreeze suggests that for summer driving, optimal cooling of the engine is obtained with only 50 per cent antifreeze. If the capacity of the raditor is 4 liters, how much coolant (in liters) must be drained and replaced with pure water to reduce the antifreeze concentration to 50 per cent?

Answer 1

answered in the first related question below.

Answer 2

To solve this problem, we need to find out how much coolant needs to be drained from the radiator and how much pure water needs to be added to achieve a concentration of 50% antifreeze.

Let's break down the information provided:

- The current solution in the radiator is 70% antifreeze and 30% water.
- The manufacturer suggests that optimal cooling of the engine is achieved with a 50% antifreeze concentration.
- The radiator has a capacity of 4 liters.

To find how much coolant should be drained, we need to calculate the difference between the current concentration and the desired concentration.

Step 1: Calculate the current amount of antifreeze in the radiator.
The current amount of antifreeze is 70% of the total solution.
Antifreeze in the radiator = 70/100 * 4 liters = 2.8 liters

Step 2: Calculate the amount of antifreeze needed for a 50% concentration.
For a 50% concentration, we want half of the volume to be antifreeze.
Antifreeze needed for 50% concentration = 50/100 * 4 liters = 2 liters

Step 3: Calculate the amount of coolant that needs to be drained.
The difference between the current amount of antifreeze and the desired amount of antifreeze.
Coolant to be drained = 2.8 liters - 2 liters = 0.8 liters

Therefore, 0.8 liters of coolant must be drained from the radiator to reduce the antifreeze concentration to 50%.

Now, to find the amount of pure water that needs to be added, we can subtract the amount of coolant drained from the radiator from its total capacity.

Amount of pure water to be added = 4 liters - 0.8 liters = 3.2 liters

Hence, 0.8 liters of coolant must be drained, and 3.2 liters of pure water should be added to reduce the antifreeze concentration to 50%.