# Maya runs 6 miles in 45 minutes. At the same rate, how many minutes would she take to run 4 miles?

## Question:

Maya runs 6 miles in 45 minutes. At the same rate, how many minutes would she take to run 4 miles?

## Ratio and Proportion:

For quantities that are know to behave proportionally to each other, the relationship between them can be used to determine on of the two given the other quantity at a different setup. For example, knowing that five people need two hours to finish a task, increasing the number of people results in less time needed to finish the same task. Why? Because there is an inverse relationship between time and number of people.

At time of 45 mins is needed to run 6 miles, at the same rate, running 4 miles, a shorter distance, requires less time. Therefore:

{eq}\begin{align*} 6\ \text{ miles} &\Leftrightarrow 45\ \text{mins}\\ 4\ \text{miles} &\Leftrightarrow ?? \text{less time}\\ \Rightarrow \text{Required Time}\ &= \frac{4\ miles}{6\ miles} \times 45\ mins\\ &= 30\ mins \end{align*} {/eq}

She would take 30 mins to run 4 miles. 