SOLUTION: When pumps, A, B, and C are running together, they can all pump 3700 gallons per hour. When only A and B are running, 2200 gallons per hour can be pumped. When only A and C are run

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Question 1156688: When pumps, A, B, and C are running together, they can all pump 3700 gallons per hour. When only A and B are running, 2200 gallons per hour can be pumped. When only A and C are running, 2400 gallons per hour can be pumped. What is the pumping capacity of each pump?
Found 3 solutions by ikleyn, VFBundy, josmiceli:
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.

From the condition, you have these 3 equations


    A + B + C = 3700    (1)

    A + B     = 2200    (2)

    A     + C = 2400    (3)


To find C, from equation (1) subtract equation (2) :  C = 3700-2200 = 1500 gallons per hour.


To find B, from equation (1) subtract equation (3) :  B = 3700-2400 = 1300 gallons per hour.


To find A, substitute the value of B= 1300 into equation (2)

    A + 1300 = 2200,  which gives you  A = 2200 - 1300 = 900 gallons per hour.

Solved.


Answer by VFBundy(438)   (Show Source): You can put this solution on YOUR website!
A + B + C = 3700
A + B = 2200
A + C = 2400

Let A + B = 2200 be B = 2200 - A
Let A + C = 2400 be C = 2400 - A

Substitute B = 2200 - A and C = 2400 - A into A + B + C = 3700:

A + (2200 - A) + (2400 - A) = 3700

Simplify and solve:

A + (2200 - A) + (2400 - A) = 3700
A + 2200 - A + 2400 - A = 3700
-A + 4600 = 3700
-A = -900
A = 900

Substitute A = 900 into A + B = 2200:

900 + B = 2200

Solve for B:

B = 1300

Substitute A = 900 into A + C = 2400:

900 + C = 2400

Solve for C:

C = 1500

The pumping capacities of each pump are:

A = 900 gallons per hour
B = 1300 gallons per hour
C = 1500 gallons per hour
Answer by josmiceli(19441)   (Show Source): You can put this solution on YOUR website!
Let R[a], R[b], and R[c] = the rates of pumping
for the 3 pumps in gallons / hr
-------------------------------------
(1)
(2)
(3)
-----------------------------------
There are 3 equations and 3 unknowns,
so it's solvable
--------------------
Subtract (2) from (1)
(1)
(2)

---------------------
Subtract (3) from (1)
(1)
(3)

----------------------
and
(3)
(3)
(3)
---------------------------
Pump A: 900 gal/hr
Pump B: 1300 gal/hr
Pump C: 1500 gal/hr
--------------------------
check:
(1)
(1)
(1)
OK

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