Question

jose ran \\(\frac{1}{3}\\) mile in 3 minutes and 15 seconds. calculate joses rate in minutes per mile; in other words, the time that it would take for him to run 1 mile. \\(\bigcirc\\) \\(9\frac{1}{4}\\) minutes per mile \\(\bigcirc\\) 9 minutes per mile \\(\bigcirc\\) \\(9\frac{3}{4}\\) minutes per mile \\(\bigcirc\\) \\(\frac{4}{39}\\) minutes per mile

Explanation:

Step1: Convert time to minutes

15 seconds is $\frac{15}{60} = \frac{1}{4}$ minutes. So 3 minutes and 15 seconds is $3 + \frac{1}{4} = 3\frac{1}{4}$ minutes.

Step2: Set up proportion to find time per mile

Let $t$ be the time per mile. We know that $\frac{1}{3}$ mile takes $3\frac{1}{4}$ minutes, so $\frac{3\frac{1}{4}}{\frac{1}{3}} = t$.

Step3: Calculate the value of t

First, convert $3\frac{1}{4}$ to improper fraction: $3\frac{1}{4} = \frac{13}{4}$. Then, $\frac{\frac{13}{4}}{\frac{1}{3}} = \frac{13}{4} \times 3 = \frac{39}{4} = 9\frac{3}{4}$ minutes per mile.

Answer:

$9\frac{3}{4}$ minutes per mile (the option with text "9$\frac{3}{4}$ minutes per mile")