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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

3 answers

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:

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

  1. 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.

can you explain it better in bullet points

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.