Question

A train travels 500 miles in 8 hours. Assuming that the train continues to travel at a constant rate, write an equation that represents this situation.
y=8x
y=2/125x
y=125/2x
y=500x

Answer 1

To determine the equation that represents the situation of a train traveling 500 miles in 8 hours at a constant rate, we first calculate the rate of travel. The rate can be calculated as:

\[
\text{Rate} = \frac{\text{Distance}}{\text{Time}} = \frac{500 \text{ miles}}{8 \text{ hours}} = 62.5 \text{ miles per hour}
\]

Now, let \( y \) represent the distance traveled (in miles) and \( x \) represent the time traveled (in hours). The relationship can be expressed with the equation:

\[
y = \text{Rate} \times x
\]

Substituting the rate we calculated:

\[
y = 62.5x
\]

However, none of the provided options include \( y = 62.5x \). Instead, we can express 62.5 as a fraction.

\[
62.5 = \frac{625}{10} = \frac{125}{2}
\]

So, the final equation can be rewritten as:

\[
y = \frac{125}{2}x
\]

Thus, the correct answer from the given options is:

\[
y = \frac{125}{2}x
\]