You are traveling home from work. You are decreasing the distance as you walk home. Your house is 41 blocks away, and you walk 3 blocks per minute. Create a linear equation that represent the situation. How many minutes will it take, to the nearest minute, to get home?

Question

A: y=41 +3x; 14 minutes
B:y=41 -3x; 14 minutes
C: y=41 3x; 13 minutes

Answer 1

To create a linear equation to represent the situation, we need to identify the variables.

Let:

• \( y \) be the distance to your house in blocks,
• \( x \) be the time in minutes.

Since you start 41 blocks away and decrease the distance as you walk, the equation will reflect that distance is decreasing with time. You walk 3 blocks per minute, so the equation will be:

\[ y = 41 - 3x \]

Now, we want to figure out how many minutes it will take to reach home, which means we want to find when \( y = 0 \):

\[ 0 = 41 - 3x \]

Solving for \( x \):

1. Add \( 3x \) to both sides: \[ 3x = 41 \]
2. Divide by 3: \[ x = \frac{41}{3} \approx 13.67 \]

To the nearest minute, this is 14 minutes.

So, the correct answer is: B: y = 41 - 3x; 14 minutes.