Question

jenny is training for a race. she ran ⅞ mile in 2⅔ minutes. how long does it take her to run each mile?

Explanation:

Step1: Identify the given values

Jenny ran \( 2\frac{3}{5} \) miles (which is \( \frac{13}{5} \) miles) in a certain number of minutes? Wait, no, the problem says "She ran \( \frac{3}{5} \) mile in 2 minutes"? Wait, no, let's re - read. Wait, the text: "Jenny is training for a race. She ran \( \frac{3}{5} \) mile in 2 minutes. How long does it take her to run each mile?" Wait, maybe the original is \( 2\frac{3}{5} \) minutes? Wait, no, let's parse the text again. The text: "Jenny is training for a race. She ran \( \frac{3}{5} \) mile in 2 minutes. How long does it take her to run each mile?" (Assuming the correct numbers: distance \( d=\frac{3}{5} \) mile, time \( t = 2 \) minutes. We need to find time per mile, \( t_{per\ mile}\))

Step2: Set up the proportion

We know that time is proportional to distance. So, if \( \frac{3}{5} \) mile takes 2 minutes, then 1 mile will take \( t \) minutes. We can set up the proportion: \( \frac{\frac{3}{5}\text{ mile}}{2\text{ minutes}}=\frac{1\text{ mile}}{t\text{ minutes}} \)

Cross - multiply: \( \frac{3}{5}\times t=2\times1 \)

Step3: Solve for t

To solve for \( t \), we have \( t = 2\div\frac{3}{5} \)

Using the rule of dividing by a fraction (multiply by its reciprocal), \( t=2\times\frac{5}{3}=\frac{10}{3}=3\frac{1}{3} \) minutes. Wait, no, wait, maybe the distance is \( 2\frac{3}{5} \) miles? Wait, the text was a bit unclear, but let's assume the correct problem: Jenny ran \( \frac{3}{5} \) mile in 2 minutes. Find time per mile.

Wait, let's re - express. If distance \( d=\frac{3}{5} \) mile, time \( t = 2 \) minutes. The rate is \( r=\frac{d}{t}=\frac{\frac{3}{5}}{2}=\frac{3}{10} \) miles per minute. But we want time per mile, which is \( \frac{1}{r}=\frac{1}{\frac{3}{10}}=\frac{10}{3}\approx3.33 \) minutes per mile.

Wait, maybe the original problem was: She ran \( 2\frac{3}{5} \) miles in some time? No, the text says "She ran \( \frac{3}{5} \) mile in 2 minutes. How long does it take her to run each mile?"

So, step - by - step:

1. Let \( x \) be the time (in minutes) to run 1 mile.
2. We know that the time per mile is constant. So, the ratio of time to distance is constant. So, \( \frac{2\text{ minutes}}{\frac{3}{5}\text{ mile}}=\frac{x\text{ minutes}}{1\text{ mile}} \)
3. Cross - multiply: \( \frac{3}{5}x = 2\times1 \)
4. Solve for \( x \): \( x=2\div\frac{3}{5}=2\times\frac{5}{3}=\frac{10}{3}=3\frac{1}{3} \) minutes.

Answer:

It takes her \( \frac{10}{3} \) (or \( 3\frac{1}{3} \)) minutes to run each mile.