To calculate how long it will take the object to travel 5 1/5 miles at a steady speed of 8 2/3 mph, we can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
First, we need to convert the mixed numbers to improper fractions.
- Convert \(8 \frac{2}{3}\) to an improper fraction:
\[ 8 \frac{2}{3} = \frac{8 \times 3 + 2}{3} = \frac{24 + 2}{3} = \frac{26}{3} \text{ mph} \]
- Convert \(5 \frac{1}{5}\) to an improper fraction:
\[ 5 \frac{1}{5} = \frac{5 \times 5 + 1}{5} = \frac{25 + 1}{5} = \frac{26}{5} \text{ miles} \]
Next, substitute these values into the time formula:
\[ \text{Time} = \frac{\frac{26}{5}}{\frac{26}{3}} \]
To divide by a fraction, we multiply by its reciprocal:
\[ \text{Time} = \frac{26}{5} \times \frac{3}{26} \]
The \(26\) in the numerator and denominator cancels out:
\[ \text{Time} = \frac{3}{5} \text{ hours} \]
Now, we convert \(\frac{3}{5}\) hours to minutes:
\[ \frac{3}{5} \times 60 \text{ minutes} = 36 \text{ minutes} \]
Therefore, it will take the object 36 minutes to travel 5 1/5 miles at a steady speed of 8 2/3 mph.