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?

Answer 1

1/A + 1/B + 1/C = 3400 , #1

1/A + 1/B = 1900
(A+B)/(AB) = 1900
1900AB = A+B
1900AB - B = A
B(1900A - 1) = A
B = A/(1900A - 1) , #2

1/A + 1/C = 2300
A+C = 2300AC
...
C = A/(2300A - 1) , #3

SUB #2 and #3 into #1

1/A + 1/(A/(1900A - 1)) + 1/A/(2300A - 1)) = 3400
1/A + (1900A - 1)/A + (2300A - 1)/A = 3400
1 + 1900A - 1 + 2300A - 1 = 3400A
800A = 1
A = 1/800

Subbing back into #2 you will get
B = 1/1100

and into #3 you will get
C = 1/1500

A's rate is 800 gal/hr
B's rate is 1100 gal/hr
C's rate is 1500 gal/hr

Answer 2

Thank you