Question

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

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:

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