Questions: What is the number of hours it would take 4 mail carriers to deliver the town's mail? The amount of time it takes mail carriers to deliver the mail in one town is inversely proportional to the number of mail carriers delivering the mail. With 8 mail carriers, it takes 6 hours to deliver the town's mail. What is the number of hours it would take 4 mail carriers to deliver the town's mail? 2 3 10 12

What is the number of hours it would take 4 mail carriers to deliver the town's mail?
The amount of time it takes mail carriers to deliver the mail in one town is inversely proportional to the number of mail carriers delivering the mail. With 8 mail carriers, it takes 6 hours to deliver the town's mail. What is the number of hours it would take 4 mail carriers to deliver the town's mail?
2
3
10
12

Transcript text: What is the number of hours it would take 4 mail carriers to deliver the town's mail? The amount of time it takes mail carriers to deliver the mail in one town is inversely proportional to the number of mail carriers delivering the mail. With 8 mail carriers, it takes 6 hours to deliver the town's mail. What is the number of hours it would take 4 mail carriers to deliver the town's mail? 2 3 10 12

Solution

Solution Steps

Step 1: Understand the relationship

The problem states that the time it takes to deliver the mail is inversely proportional to the number of mail carriers. This means: \[ T \propto \frac{1}{N} \] where \( T \) is the time and \( N \) is the number of mail carriers.

Step 2: Set up the equation

Since \( T \) is inversely proportional to \( N \), we can write: \[ T = \frac{k}{N} \] where \( k \) is a constant.

Step 3: Find the constant \( k \)

We are given that when \( N = 8 \), \( T = 6 \). Substitute these values into the equation to solve for \( k \): \[ 6 = \frac{k}{8} \] \[ k = 6 \times 8 = 48 \]

Step 4: Solve for \( T \) when \( N = 4 \)

Now, substitute \( N = 4 \) and \( k = 48 \) into the equation: \[ T = \frac{48}{4} = 12 \]