To find out how long it will take an object to travel a certain distance at a steady speed, you can use the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]
In this case, the distance is \(5 \frac{1}{5}\) miles and the speed is \(8 \frac{2}{3}\) miles per hour.
First, let's convert both mixed numbers to improper fractions.
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Convert \(5 \frac{1}{5}\) to an improper fraction:
- \(5 \times 5 + 1 = 25 + 1 = 26\)
- So, \(5 \frac{1}{5} = \frac{26}{5}\) miles.
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Convert \(8 \frac{2}{3}\) to an improper fraction:
- \(8 \times 3 + 2 = 24 + 2 = 26\)
- So, \(8 \frac{2}{3} = \frac{26}{3}\) miles per hour.
Now substitute these values into the formula:
\[ \text{Time} = \frac{\frac{26}{5}}{\frac{26}{3}} \]
To divide by a fraction, multiply by its reciprocal:
\[ \text{Time} = \frac{26}{5} \times \frac{3}{26} \]
The \(26\) cancels out:
\[ \text{Time} = \frac{3}{5} \text{ hours} \]
Now convert \(\frac{3}{5}\) hours into minutes. Since there are 60 minutes in an hour:
\[ \frac{3}{5} \times 60 = \frac{180}{5} = 36 \text{ minutes} \]
Therefore, it will take the object 36 minutes to travel \(5 \frac{1}{5}\) miles at a steady speed of \(8 \frac{2}{3}\) miles per hour.
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