Question

An object is traveling at a steady speed of 8 2/3 miles per hour how long will it take the object to travel 5 1/5 miles

Answer 1

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.

1. 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.

2. 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.