Questions: MATH099 - Week 2: Solve applications using proportions Week 2: Solve applications using proportions Question Katie runs 3 miles in 26 minutes. At this pace, how long will it take Katie to run 13.1 miles? Round to the nearest minute. Provide your answer below: minutes FEEDBACK MORE INSTRUCTION SUBMIT

Solution Steps

To solve this problem, we can set up a proportion based on the given information. We know that Katie runs 3 miles in 26 minutes. We need to find out how long it will take her to run 13.1 miles. We can set up the proportion as follows:

\[ \frac{3 \text{ miles}}{26 \text{ minutes}} = \frac{13.1 \text{ miles}}{x \text{ minutes}} \]

We can then solve for \( x \) by cross-multiplying and dividing.

We know that Katie runs \(3\) miles in \(26\) minutes. We need to find the time \(x\) it takes her to run \(13.1\) miles. We can set up the proportion as follows:

\[ \frac{3 \text{ miles}}{26 \text{ minutes}} = \frac{13.1 \text{ miles}}{x \text{ minutes}} \]

Cross-multiplying gives us:

\[ 3x = 26 \times 13.1 \]

Calculating the right side:

\[ 3x = 341.6 \]

Now, divide both sides by \(3\):

\[ x = \frac{341.6}{3} \approx 113.86666666666667 \]

Rounding \(113.86666666666667\) to the nearest minute gives us:

\[ x \approx 114 \]

Final Answer