We are asked to determine how long it will take an object to travel 5 and $\frac{1}{5}$ miles at a steady speed of 8 and $\frac{2}{3}$ miles per hour.

Step 1: Convert mixed numbers to improper fractions

The speed is $8 \frac{2}{3}$ miles per hour, and the distance is $5 \frac{1}{5}$ miles.

• For $8 \frac{2}{3}$, convert it to an improper fraction: $8 \frac{2}{3} = \frac{8 \times 3 + 2}{3} = \frac{24 + 2}{3} = \frac{26}{3}$

• For $5 \frac{1}{5}$, convert it to an improper fraction: $5 \frac{1}{5} = \frac{5 \times 5 + 1}{5} = \frac{25 + 1}{5} = \frac{26}{5}$

Step 2: Use the formula for time

We can use the formula: $\text{Time} = \frac{\text{Distance}}{\text{Speed}}$ Substitute the improper fractions: $\text{Time} = \frac{\frac{26}{5}}{\frac{26}{3}} = \frac{26}{5} \times \frac{3}{26} = \frac{3}{5}$

Step 3: Simplify the result

The time is $\frac{3}{5}$ hours.

Final Answer:

The object will take $\frac{3}{5}$ hours (or 36 minutes) to travel $5 \frac{1}{5}$ miles.

Would you like more details or have any questions? Here are five related questions for further practice:

1. What is the time taken if the distance is doubled but the speed remains the same?
2. How would the time change if the speed is halved and the distance remains the same?
3. Convert $\frac{3}{5}$ hours into minutes.
4. If the object were traveling at 10 miles per hour, how long would it take to travel $5 \frac{1}{5}$ miles?
5. How much distance would the object cover in 1 hour at a speed of $8 \frac{2}{3}$ miles per hour?

Tip: When dealing with mixed numbers, always convert them to improper fractions for easier manipulation in equations.