It takes Julian 1/2

Question

hour to walk 2 miles. He decides to start working in his spare time, but because he wants to make sure he has enough time to go a desired distance he created the data table. Determine the constant of proportionality, y/x
.

Answer 1

To determine the constant of proportionality \( \frac{y}{x} \), we first need to understand what \( y \) and \( x \) represent in this scenario.

From the problem, we know that Julian takes \( \frac{1}{2} \) hour (or 30 minutes) to walk 2 miles.

Let's define the variables:

• Let \( x \) be the time in hours.
• Let \( y \) be the distance in miles.

From the information provided:

• In \( \frac{1}{2} \) hour, Julian walks 2 miles.

So we can substitute these values into the formula for the constant of proportionality \( \frac{y}{x} \):

\[ \frac{y}{x} = \frac{2 \text{ miles}}{\frac{1}{2} \text{ hour}} = 2 \div \left( \frac{1}{2} \right) \]

Calculating the right side:

\[ 2 \div \left( \frac{1}{2} \right) = 2 \times 2 = 4 \]

Thus, the constant of proportionality \( \frac{y}{x} \) is \( 4 \).

This means that Julian walks at a rate of 4 miles per hour.