Question 843673: (I'm stuck on this question. Can you please help?)
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?
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Using A, B, and C as the rates in gallons per hour for each of the pump named the same, the rates of any pumps operating at the same time are simply additive. This allows three equations for the three combinations given in the description.
System:
A+B+C=3400
A+B=1900
A+C=2300
My method was to set up the matrix and to use just enough row operations to be able to back-substitute; although you could try using substitutions and resolving resulting equations in the old style if that were all you knew.
Matrix corresponding to the system listed above is
( 1, 1, 1, 3400 )
( 1, 1, 0, 1900 )
( 1, 0, 1, 2300 )
I omit the steps here, but here then are the results from the steps:
ANSWER:
-
-
Notice that C is NEGATIVE, which means that pump C does NOT fill the tank, but
REMOVES liquid from the tank.
|
|
|
