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.
- Dividing the coefficients:
\[ \frac{9.21}{5.72} \approx 1.607 \]
- Dividing the powers of ten:
\[ \frac{10^7}{10^4} = 10^{7-4} = 10^3 \]
- Combining these results:
\[ \text{Time} \approx 1.607 \times 10^3 \text{ hours} \]
- 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:
\[ \boxed{1607} \text{ hours} \]