Question

Miguel bikes 23 km per hour and starts at mile 10. Gabby bikes 28 km per hour and starts at mile 0. Which system of linear equations represents this situation?
Group of answer choices

Gabby:

Miguel:

Miguel:

Gabby:

Miguel:

Gabby:

Miguel:

Gabby:

Answer 1

Let's define the variables to represent the situation:

- Let \( t \) be the time in hours.
- Let \( d_m \) be the distance that Miguel has traveled.
- Let \( d_g \) be the distance that Gabby has traveled.

### For Miguel:
- Miguel starts at mile 10 and bikes at a speed of 23 km/h.
The equation representing Miguel's position over time can be expressed as:
\[
d_m = 10 + 23t
\]

### For Gabby:
- Gabby starts at mile 0 and bikes at a speed of 28 km/h.
The equation representing Gabby's position over time can be expressed as:
\[
d_g = 0 + 28t
\]
or simply
\[
d_g = 28t
\]

### System of Linear Equations
Now that we have both equations, we can write the system of equations:

1. For Miguel:
\[
d_m = 10 + 23t
\]

2. For Gabby:
\[
d_g = 28t
\]

So, the complete system of linear equations representing this situation is:
\[
\begin{align*}
d_m & = 10 + 23t \\
d_g & = 28t
\end{align*}
\]