When three pumps, A, B, and C, are running together, they can pump 3400 gal per hour. When only A, and B are running, 1900 gal per hour can be pumped. When only A and C are running, 2300 gal per hour can be pumped. What is the pumping capacity of each pump?
What is the pumping capacity of A___GAL PER HOUR?
What is the pumping capacity of B___GAL PER HOUR?
What is the pumping capacity of C___GAL PER HOUR?
what is your answer?
A + B + C = 3400
-----------------
A + B = 1900
A + C = 2300
------------subtract
B-C = -400
B = C - 400
A + ( C-400) + C = 3400
A + 2 C = 3800
but
A + 1 C = 2300
---------------- subtract
C = 1500
then A = 2300 - 1500 = 800
B = 1500-400 = 1100
To find the pumping capacity of each pump, we can set up a system of equations based on the given information.
Let's denote the pumping capacity of pump A as A (in gal per hour), pump B as B, and pump C as C.
From the first given statement, when all three pumps are running together, their combined pumping capacity is 3400 gal per hour. Thus, we can write the equation:
A + B + C = 3400 -- Equation 1
From the second given statement, when only pumps A and B are running, their combined pumping capacity is 1900 gal per hour. So we can write:
A + B = 1900 -- Equation 2
Similarly, from the third given statement, when only pumps A and C are running, their combined pumping capacity is 2300 gal per hour, resulting in the equation:
A + C = 2300 -- Equation 3
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve using the method of substitution:
1. Rearrange Equation 2 to express B in terms of A: B = 1900 - A.
2. Substitute B in Equation 1 with its expression from Equation 2: A + (1900 - A) + C = 3400.
3. Simplify the equation: 1900 + C = 3400.
4. Solve for C: C = 3400 - 1900 = 1500.
Now we know the pumping capacity of pump C is 1500 gal per hour.
To find the pumping capacity of pump A, we can substitute the value of C into Equation 3:
A + 1500 = 2300.
Solving for A: A = 2300 - 1500 = 800.
Therefore, the pumping capacity of pump A is 800 gal per hour.
To find the pumping capacity of pump B, we can substitute the value of C into Equation 1:
A + B + 1500 = 3400.
Substituting the value of A from Equation 2: 1900 + B + 1500 = 3400.
Simplifying the equation: B + 3400 = 3400.
Solving for B: B = 3400 - 3400 = 0.
Therefore, the pumping capacity of pump B is 0 gal per hour. (This indicates that pump B is not contributing to the pumping capacity when all three pumps are running together.)
In conclusion:
- Pump A has a pumping capacity of 800 gal per hour.
- Pump B has a pumping capacity of 0 gal per hour.
- Pump C has a pumping capacity of 1500 gal per hour.