An athlete can swim 500 meters in a nearby lake in 9.2 minutes. At this same rate, estimate the amount of time it will take her to swim one mile ( 1609 meters). It will take the athlete approximately $$ \square $$ minutes to swim one mile. (Round to the nearest tenth as needed.)

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Given that the athlete swims $$500$$ meters in $$9.2$$ minutes, her rate is

$$
\text{Rate} = \frac{500 \text{ meters}}{9.2 \text{ minutes}}.
$$

To find the time $$t$$ required to swim $$1609$$ meters, we set up the proportion

$$
t = \frac{1609 \text{ meters}}{\text{Rate}} = \frac{1609}{500} \times 9.2.
$$

Calculating the factor first:

$$
\frac{1609}{500} \approx 3.218.
$$

Then multiplying by $$9.2$$ minutes:

$$
t \approx 3.218 \times 9.2 \approx 29.6 \text{ minutes}.
$$

Thus, it will take the athlete approximately $$29.6$$ minutes to swim one mile.
It will take the athlete approximately 29.6 minutes to swim one mile.

An athlete can swim 500 meters in a nearby lake in 9.2 minutes. At this same rate, estimate the amount of time it will take her to swim one mile ( 1609 meters). It will take the athlete approximately \( \square \) minutes to swim one mile. (Round to the nearest tenth as needed.)

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