The distance from Earth to Mercury is 9, point, 2, 1, times, 10, to the power 7

Question

kilometers. How long would it take a rocket, traveling at 5, point, 7, 2, times, 10, to the power 4

kilometers per hour to travel from Earth to Mercury? Round your answer to the nearest whole number of hours.

Answer 1

To find the time it takes for a rocket to travel from Earth to Mercury, we can use the formula for time:

\[ \text{Time} = \frac{\text{Distance}}{\text{Speed}} \]

Given:

• Distance from Earth to Mercury: \( 9.21 \times 10^7 \) kilometers
• Speed of the rocket: \( 5.72 \times 10^4 \) kilometers per hour

Now, substituting the values into the formula:

\[ \text{Time} = \frac{9.21 \times 10^7 \text{ km}}{5.72 \times 10^4 \text{ km/h}} \]

Now, let's calculate it step-by-step.

1. Dividing the coefficients:

\[ \frac{9.21}{5.72} \approx 1.607 \]

2. Dividing the powers of ten:

\[ \frac{10^7}{10^4} = 10^{7-4} = 10^3 \]

3. Combining these results:

\[ \text{Time} \approx 1.607 \times 10^3 \text{ hours} \]

4. Converting \( 1.607 \times 10^3 \) to a number:

\[ 1.607 \times 10^3 = 1607 \text{ hours} \]

Finally, rounding to the nearest whole number, we find that the time it would take for the rocket to travel from Earth to Mercury is:

\[ \boxed{1607} \text{ hours} \]