When three pumps A B and C are running together they can pum

When three pumps, A, B and C, are running together, they can pump 3200 gal per hour. When only A and B are running,1900 gal per hour can be pumped. When only A and C are running, 2000 gal per hour can be pumped. What is the pumping capacity of each pump?

A =

B=

C=

Solution

The three pumping rates will be shown as: A, B & C.

Running together they pump 3200 gallons per hour.
A + B + C = 3200
.
We also are told:
A + B = 1900
which means
B = 1900 - A
.
We also are told:
A + C = 2000
So,
C = 2000 - A

Looking back at the first equation, we can substitute for B and C.
A = A
B = 1900-A
C = 2000-A
A +1900-A + 2000-A = 3200
Collecting terms:
A-2A + 3900 = 3200
Simplify and subtract 3800 from both sides
-A = -700
Multiply both sides by -1
A = 700

That means
B = 1900-700
B = 1200
and
C = 2000-700
C = 1300

A + B + C = 700 + 1200 + 1300
A + B + C = 3200

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