(Can someone please help me with this question?)
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?
see
http://www.jiskha.com/display.cgi?id=1392932194
To find the pumping capacity of each pump, we can set up a system of equations based on the given information.
Let's assign variables to the pumping capacity of each pump:
Let the pumping capacity of pump A be 'x' gallons per hour.
Let the pumping capacity of pump B be 'y' gallons per hour.
Let the pumping capacity of pump C be 'z' gallons per hour.
Now, let's form equations based on the given information:
Equation 1: A + B + C = 3400 (When all three pumps A, B, and C are running together, they can pump 3400 gallons per hour.)
Equation 2: A + B = 1900 (When only pumps A and B are running, they can pump 1900 gallons per hour.)
Equation 3: A + C = 2300 (When only pumps A and C are running, they can pump 2300 gallons per hour.)
To find the pumping capacity of each pump, we need to solve this system of equations simultaneously.
One way to solve this system of equations is by using substitution.
Step 1: Solve Equation 2 for A in terms of B:
A = 1900 - B
Step 2: Substitute this value of A in Equation 3:
(1900 - B) + C = 2300
Step 3: Simplify Equation 3:
C = 2300 - 1900 + B
C = 400 + B
Step 4: Substitute the values of A and C in Equation 1:
(1900 - B) + B + (400 + B) = 3400
Step 5: Simplify Equation 1:
1900 - B + B + 400 + B = 3400
2300 + B = 3400
Step 6: Solve for B:
B = 3400 - 2300
B = 1100
Now that we have the value of B, we can substitute it back into Equation 1 to find A:
A + 1100 + (400 + 1100) = 3400
A + 2100 = 3400
A = 3400 - 2100
A = 1300
Finally, plug the values of A and B into Equation 3 to find C:
1300 + C = 2300
C = 2300 - 1300
C = 1000
Therefore, the pumping capacity of pump A is 1300 gallons per hour (Gal/h), the pumping capacity of pump B is 1100 Gal/h, and the pumping capacity of pump C is 1000 Gal/h.