Question

a person runs 3 miles in 40 min. what is the speed in mph?
\\(\frac{1}{2} = \frac{x}{9}\\)

Explanation:

Step1: Cross - multiply the proportion

Given the proportion $\frac{1}{2}=\frac{x}{9}$, cross - multiplying (which means multiplying the numerator of the left - hand side by the denominator of the right - hand side and setting it equal to the denominator of the left - hand side multiplied by the numerator of the right - hand side) gives us $2\times x = 1\times9$.

Step2: Solve for x

We have the equation $2x = 9$. To solve for $x$, we divide both sides of the equation by 2. So, $x=\frac{9}{2}=4.5$. But wait, let's check the original speed problem. The person runs 3 miles in 40 minutes. First, convert 40 minutes to hours. Since 1 hour = 60 minutes, 40 minutes $=\frac{40}{60}=\frac{2}{3}$ hours. Speed $s=\frac{d}{t}$, where $d = 3$ miles and $t=\frac{2}{3}$ hours. So $s=\frac{3}{\frac{2}{3}}=3\times\frac{3}{2}=\frac{9}{2}=4.5$ mph. The proportion $\frac{1}{2}=\frac{x}{9}$: if we consider the time - distance ratio, 40 minutes is $\frac{2}{3}$ of an hour? Wait, maybe the proportion is set up as $\frac{3}{40}=\frac{x}{60}$ (since we want miles per hour, 60 minutes in an hour). Cross - multiplying: $40x = 3\times60=180$, then $x=\frac{180}{40}=4.5$. The given proportion $\frac{1}{2}=\frac{x}{9}$: solving it gives $x = 4.5$, which matches the speed calculation.

Answer:

The value of $x$ is $4.5$ (and the speed is $4.5$ mph).