To simplify the expression \(\frac{27.0 \text{ meters}}{1.5 \text{ meters/2 minutes}}\), we'll start by rewriting the denominator.
The denominator, \(1.5 \text{ meters/2 minutes}\), can be rewritten as:
\[ 1.5 \text{ meters/2 minutes} = \frac{1.5 \text{ meters}}{2 \text{ minutes}} = 0.75 \text{ meters/minute} \]
Now, the original expression becomes:
\[ \frac{27.0 \text{ meters}}{0.75 \text{ meters/minute}} \]
To simplify this expression, we can multiply by the reciprocal of the denominator:
\[ \frac{27.0 \text{ meters}}{0.75 \text{ meters/minute}} = 27.0 \text{ meters} \times \frac{1 \text{ minute}}{0.75 \text{ meters}} = \frac{27.0 \text{ meters}}{0.75 \text{ meters}} \times 1 \text{ minute} \]
The "meters" unit cancels out:
\[ = \frac{27.0}{0.75} \text{ minutes} \]
Now, calculating \(\frac{27.0}{0.75}\):
\[ \frac{27.0}{0.75} = 36 \text{ minutes} \]
Thus, we have:
\[ 36 \text{ minutes} \]
If the problem states that this corresponds to 18 descents, we can establish that each descent takes:
\[ \frac{36 \text{ minutes}}{18 \text{ descents}} = 2 \text{ minutes/ descent} \]
So in conclusion, the simplified expression shows that 27.0 meters corresponds to 36 minutes, which results in 18 descents taking place.
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