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(52835)   (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):
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