The radiator in a car is filled with a solution of 60% antifreeze and 40% water. The manufacturer of the the antifreeze suggests that, for summer diving, optimal cooling of the engine is obtained with only 50% antifreeze. If the capacity of the radiator is 3.6 liters, how much coolant should be drained and replaced with waterto reduce antifreeze concentration to the recommended level.
presently is
.6 * 3.6 = 2.16 af
.4 * 3.6 = 1.44 h2o
should be
.5 * 3.6 = 1.8 af
1.8 h2o
add x liters water
take out .6 x af and .4 x water
new af = 1.8 = 2.16 - .6 x
so
.6 x = .36
x = .6
==============
check
new water = 1.44 - .4(.6) + .6
= 1.8 whew
To solve this problem, we need to find out how much coolant needs to be drained and replaced with water in order to reduce the antifreeze concentration to the recommended level.
Let's assume 'x' represents the amount of coolant that needs to be drained and replaced with water in liters.
Given:
- The radiator capacity is 3.6 liters.
- The current solution in the radiator is 60% antifreeze and 40% water.
- The recommended solution for optimal cooling in summer is 50% antifreeze and 50% water.
To solve for 'x', we can set up the following equation based on the amount of antifreeze in the radiator:
0.6 * (3.6 - x) = 0.5 * 3.6
Now, let's solve for 'x':
0.6 * (3.6 - x) = 0.5 * 3.6
Multiply both sides by 10 to get rid of the decimal point:
6 * (3.6 - x) = 5 * 3.6
Expand the equation:
21.6 - 6x = 18
Subtract 21.6 from both sides:
-6x = 18 - 21.6
Simplify:
-6x = -3.6
Divide both sides by -6 to isolate 'x':
x = -3.6 / -6
Simplify:
x = 0.6
Therefore, you need to drain and replace 0.6 liters of coolant with water to reduce the antifreeze concentration to the recommended level.
To find out how much coolant should be drained and replaced with water to reduce the antifreeze concentration to the recommended level, we can follow these steps:
Step 1: Calculate the initial amount of antifreeze in the radiator.
The radiator has a capacity of 3.6 liters, and it is filled with a solution that is 60% antifreeze. So, the initial amount of antifreeze in the radiator can be calculated as:
Initial antifreeze amount = 3.6 liters * 60% = 2.16 liters
Step 2: Calculate the desired amount of antifreeze for summer driving.
The manufacturer suggests that the optimal cooling is obtained with 50% antifreeze. So, the desired amount of antifreeze for summer driving can be calculated as:
Desired antifreeze amount = 3.6 liters * 50% = 1.8 liters
Step 3: Determine the difference between the initial and desired antifreeze amounts.
Difference = Initial antifreeze amount - Desired antifreeze amount
Difference = 2.16 liters - 1.8 liters = 0.36 liters
Therefore, to reduce the antifreeze concentration to the recommended level, approximately 0.36 liters of coolant should be drained from the radiator and replaced with water.