To solve the problem, let's denote the time it takes Owen to clean 100 windows by himself as \( t \) minutes. Since Greg is 1.7 times faster than Owen, his cleaning time for 100 windows can be expressed as:
\[ \text{Time for Greg} = \frac{t}{1.7} \quad \text{(in minutes)} \]
Next, we can determine their individual rates of cleaning windows:
- Owen's rate of cleaning is \( \frac{100 , \text{windows}}{t , \text{minutes}} \) or \( \frac{100}{t} \) windows per minute.
- Greg's rate of cleaning is \( \frac{100 , \text{windows}}{\frac{t}{1.7}} \) or \( \frac{100 \times 1.7}{t} = \frac{170}{t} \) windows per minute.
When they work together, their combined rate of cleaning is:
\[ \frac{100}{t} + \frac{170}{t} \]
Combining these rates gives us:
\[ \frac{100 + 170}{t} = \frac{270}{t} \quad \text{(windows per minute)} \]
In the problem, it is given that they clean 100 windows together in 39 minutes. Therefore, their combined rate can also be computed as:
\[ \frac{100 , \text{windows}}{39 , \text{minutes}} \approx \frac{100}{39} \quad \text{(windows per minute)} \]
Now we set the two expressions for the combined rate equal to each other:
\[ \frac{270}{t} = \frac{100}{39} \]
To solve for \( t \), we cross-multiply:
\[ 270 \cdot 39 = 100 \cdot t \]
Calculating the left side:
\[ 270 \cdot 39 = 10530 \]
Thus, we have:
\[ 100t = 10530 \]
Now, dividing both sides by 100 gives:
\[ t = \frac{10530}{100} = 105.3 \]
Therefore, it would take Owen approximately 105.3 minutes to clean 100 windows by himself. Rounding to the nearest tenth, the final answer is:
\[ \boxed{105.3} \] minutes.
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