High School

**Problem 1:**
A duct from a furnace forks into two ducts. The 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 1,900 cu ft/min in the first duct, the flow is 900 cu ft/min in the second duct.
b. The flow is 1,550 cu ft/min in the first duct, the flow is 1,250 cu ft/min in the second duct.
c. The flow is 1,700 cu ft/min in the first duct, the flow is 1,100 cu ft/min in the second duct.
d. The flow is 1,100 cu ft/min in the first duct, the flow is 1,900 cu ft/min in the second duct.
e. The flow is 1,600 cu ft/min in the first duct, the flow is 1,200 cu ft/min in the second duct.

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**Problem 2:**
A dairyman wants to make 237 lb of 14%-butterfat cream. How many pounds of 40%-butterfat cream and how many pounds of 1%-butterfat milk must he mix?

a. 82 lb of 40%-butterfat cream, 155 lb of 1%-butterfat milk.
b. 74 lb of 40%-butterfat cream, 163 lb of 1%-butterfat milk.
c. 158 lb of 40%-butterfat cream, 79 lb of 1%-butterfat milk.
d. 79 lb of 40%-butterfat cream, 158 lb of 1%-butterfat milk.
e. 81 lb of 40%-butterfat cream, 156 lb of 1%-butterfat milk.

Answer :

1.Flow in Ducts: 1,600 cu ft/min in the first duct, 1,200 cu ft/min in the second duct. So the correct option is e.

2.Mixing Butterfat Cream and Milk: 79 lb of 40%-butterfat cream, 158 lb of 1%-butterfat milk. So the correct option is d.

1. Flow in Ducts:

Let x be the flow in the first duct.

Then, the flow in the second duct would be x + 400 cubic feet per minute.

The total flow is 2,800 cubic feet per minute, so we can write the equation:

x + (x + 400) = 2800

Solving for x:

2x + 400 = 2800

2x = 2400

x = 1200

The flow in the first duct (x) is 1200 cubic feet per minute.

The flow in the second duct (x + 400) is 1600 cubic feet per minute.

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

2. Mixing Butterfat Cream and Milk:

Let x be the pounds of 40%-butterfat cream to mix.

Then, the pounds of 1%-butterfat milk to mix would be (237 - x) since the total amount is 237 lb.

The equation can be set up based on the butterfat content:

0.4x + 0.01(237 - x) = 0.14(237)

Solving for x:

0.4x + 2.37 - 0.01x = 33.18

0.39x = 30.81

x = 79

So, the dairyman needs to mix 79 pounds of 40%-butterfat cream and (237 - 79) = 158 pounds of 1%-butterfat milk.

Therefore, the correct answer is: d. 79 lb of 40%-butterfat cream, 158 lb of 1%-butterfat milk.

To know more about Ducts:-

https://brainly.com/question/12975642

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