3 inlet pipes A,B and C can be used to fill 1000m^3 water storage tank . When 3 pipes are in operation,the tank can be filled in 10hours .When only pipes A and B are used,the time increases to 20 hours. With pipe A and C, the tank can be filled in 12.5 gourde. By using Gauss Jordan Elimination method, find the individual flow rate for each of the three pipe.
1/a + 1/b + 1/c = 1/10
1/a + 1/b = 1/20
1/a + 1/c = 2/25
Now just solve normally use GJ, but use 1/a, 1/b, 1/c as your variables. When you get the results, the values for a,b,c are the reciprocals.
To find the individual flow rate for each of the three pipes using Gauss Jordan Elimination method, we need to set up a system of equations based on the given information.
Let's denote the flow rate of pipe A as a cubic meters per hour, the flow rate of pipe B as b cubic meters per hour, and the flow rate of pipe C as c cubic meters per hour.
From the given information, we can set up the following equations:
Equation 1: 10a + 10b + 10c = 1000
Equation 2: 20a + 20b = 1000
Equation 3: 12.5a + 12.5c = 1000
Now, let's solve this system of equations using Gauss Jordan Elimination method:
Step 1: Write the augmented matrix:
10 10 10 | 1000
20 20 0 | 1000
12.5 0 12.5 | 1000
Step 2: Simplify the matrix:
Divide Row 1 by 10:
1 1 1 | 100
Divide Row 2 by 20:
1 1 0 | 50
Divide Row 3 by 12.5:
1 0 1 | 80
Step 3: Perform row operations to create zeros in the first and third columns:
Row 2 - Row 1:
0 0 -1 | -50
Row 3 - Row 1:
0 -1 0 | 30
Step 4: Simplify the matrix:
1 1 1 | 100
0 0 -1 | -50
0 -1 0 | 30
Step 5: Perform row operations to create zeros in the second column:
Row 2 + Row 3:
0 -1 -1 | -20
Step 6: Simplify the matrix:
1 1 1 | 100
0 -1 -1 | -20
0 -1 0 | 30
Step 7: Perform row operations to create zeros in the third column:
Row 2 + Row 3:
0 -1 -1 | -20
Step 8: Simplify the matrix:
1 1 1 | 100
0 -1 -1 | -20
0 0 -1 | 10
Step 9: Perform row operations to create ones in the diagonal:
Row 2 * (-1):
0 1 1 | 20
Row 3 * (-1):
0 0 1 | -10
Step 10: Simplify the matrix:
1 1 1 | 100
0 1 1 | 20
0 0 1 | -10
Step 11: Perform row operations to create zeros above the ones in the diagonal:
Row 2 - Row 3:
0 1 0 | 30
Row 1 - Row 3:
1 1 0 | 110
Step 12: Simplify the matrix:
1 1 0 | 110
0 1 0 | 30
0 0 1 | -10
Step 13: Now, we have the simplified matrix in row echelon form. Extracting the solution from the matrix:
a = 110 - 1 = 109
b = 30 - 0 = 30
c = -10 - 0 = -10
However, having a negative flow rate for pipe C does not make sense in this context.
Since pipe C cannot have a negative flow rate, there might be an error or inconsistency in the given information or calculations.
Please double-check the calculations or provide additional information to resolve the inconsistency.