Question

You are travelling ho me 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 represents the situation. How many minutes will it take, to the nearest minute, to get home?
Responses

y = 41 - 3x; 13 minutes

y = 41 + 3x; 14 minutes

y = 41 + 3x; 13 minutes

y = 41 - 3x; 14 minutes

Answer 1

To create a linear equation that represents the situation described, let's define our variables:

- \( y \) represents the distance to your house in blocks (which starts at 41 blocks).
- \( x \) represents the time in minutes.

Since you are walking towards home, the distance decreases as time goes on. You walk 3 blocks per minute, so for every minute that passes, the distance to your house decreases by 3 blocks. Thus, the equation that models this situation is:

\[ y = 41 - 3x \]

Now, we will find out how many minutes it will take to get home. You reach home when \( y = 0 \):

\[
0 = 41 - 3x
\]

Solving for \( x \):

\[
3x = 41
\]
\[
x = \frac{41}{3} \approx 13.67
\]

Rounding to the nearest minute, it will take approximately 14 minutes to get home.

The correct response, summarizing this information, is:

**y = 41 - 3x; 14 minutes**.