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A duct from a furnace forks into two ducts. The total air coming into the two ducts was 2,800 cubic feet per minute. If one duct took 400 cubic feet per minute more than the other duct, what was the flow in cubic feet per minute (cu ft/min) in each duct?

a. The flow is 1,100 cu ft/min in the first duct; the flow is 1,900 cu ft/min in the second duct.
b. The flow is 1,900 cu ft/min in the first duct; the flow is 900 cu ft/min in the second duct.
c. The flow is 1,600 cu ft/min in the first duct; the flow is 1,200 cu ft/min in the second duct.
d. The flow is 1,700 cu ft/min in the first duct; the flow is 1,100 cu ft/min in the second duct.
e. The flow is 1,550 cu ft/min in the first duct; the flow is 1,250 cu ft/min in the second duct.

Answer :

Final answer:

By setting up an equation and solving for the flow rates, we find that the first duct has a flow of 1,200 cu ft/min, and the second duct has a flow of 1,600 cu ft/min, which confirms answer choice c as correct.

Explanation:

The problem you're working on involves splitting a total flow rate of 2,800 cubic feet per minute (cu ft/min) of air into two separate ducts, with one duct receiving 400 cu ft/min more than the other. To solve this, we use the algebraic method of setting up an equation.

Let's denote the flow in the first duct as 'x' cu ft/min. Then the flow in the second duct would be 'x + 400' cu ft/min, since it's given that the second duct receives 400 cu ft/min more air than the first.

Since the total flow rate into both ducts is 2,800 cu ft/min, we can write the equation as follows:

x + (x + 400) = 2,800

This simplifies to:

2x + 400 = 2,800

Subtracting 400 from both sides gives:

2x = 2,400

And dividing by 2:

x = 1,200

So the flow in the first duct is 1,200 cu ft/min and the flow in the second duct, which is 400 cu ft/min more, is:

1,200 + 400 = 1,600 cu ft/min

Therefore, the answer is c: The flow is 1,600 cu ft/min in the first duct, and the flow is 1,200 cu ft/min in the second duct.

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