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

Answer 1

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.

1. Convert $8\frac{2}{3}$ to an improper fraction:

$$8\frac{2}{3}=\frac{8\times 3+2}{3}=\frac{24+2}{3}=\frac{26}{3}\text{ mph}$$

2. 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.

Answer 2

can you explain it better in bullet points

Answer 3

Sure! Here’s the explanation broken down into clear bullet points:

1. Identify the Information Given:

   • Speed: $8\frac{2}{3}$ mph.
   • Distance: $5\frac{1}{5}$ miles.

2. Convert Mixed Numbers to Improper Fractions:

   • Convert speed:
     • $8\frac{2}{3}=\frac{8\times 3+2}{3}=\frac{24+2}{3}=\frac{26}{3}$ mph.
   • Convert distance:
     • $5\frac{1}{5}=\frac{5\times 5+1}{5}=\frac{25+1}{5}=\frac{26}{5}$ miles.

3. Use the Formula for Time:

   • Formula: $\text{Time}=\frac{\text{Distance}}{\text{Speed}}$.
   • Substitute the values:
     • $\text{Time}=\frac{\frac{26}{5}}{\frac{26}{3}}$.

4. Divide Fractions:

   • To divide by a fraction, multiply by its reciprocal:
     • $\text{Time}=\frac{26}{5}\times \frac{3}{26}$.
   • The $26$ cancels out:
     • $\text{Time}=\frac{3}{5}$ hours.

5. Convert Hours to Minutes:

   • Since there are 60 minutes in an hour:
     • $\frac{3}{5}\text{ hours}\times 60\text{ minutes}=36\text{ minutes}$.

6. Final Answer:

   • It will take 36 minutes for the object to travel 5 1/5 miles at a speed of 8 2/3 mph.