Question

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 represents the situation. How many minutes will it take, to the nearest minute, to get home?(1 point)
Responses

y=41−3x;
14 minutes
14 minutes

y=41−3x;
13 minutes
13 minutes

y=41+3x;
13 minutes
13 minutes

y=41+3x;
14 minutes

Answer 1

To create a linear equation representing the situation, we can define the variables as follows:

- Let \( y \) represent the distance from your house in blocks.
- Let \( x \) represent the time in minutes.

Since you start 41 blocks away from your house and walk toward it at a rate of 3 blocks per minute, the equation would be:

\[
y = 41 - 3x
\]

This indicates that the distance to your house decreases by 3 blocks for every minute you walk.

To find out how many minutes it will take to get home, we need to determine when \( y = 0 \) (which signifies that you are home):

\[
0 = 41 - 3x
\]

Now, solve for \( x \):

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

Rounding to the nearest minute gives us approximately 14 minutes.

Thus, the correct response is:

y = 41 − 3x; 14 minutes