To solve how long Ananya's practice session lasts while swimming 10 miles at an average speed that is three times slower than \(m\) miles per hour, we first need to determine her speed.
If Ananya swims at an average speed of \(m\) miles per hour, being three times slower means her speed is:
\[ \text{Speed} = \frac{m}{3} \text{ miles per hour} \]
Next, we need to find out how long it takes her to swim 10 miles at this speed. We can use the formula for time, which is:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this case:
\[ \text{Time} = \frac{10 \text{ miles}}{\frac{m}{3} \text{ miles per hour}} \]
This can be simplified by multiplying by the reciprocal of the speed:
\[ \text{Time} = 10 \text{ miles} \times \frac{3}{m} \text{ hours per mile} \]
Calculating this gives:
\[ \text{Time} = \frac{30}{m} \text{ hours} \]
Thus, the duration of Ananya's practice session is:
\[ \frac{30}{m} \text{ hours} \]
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