The distance from Earth to Mercury is 9, point, 2, 1, times, 10, to the power 79.21×10
7
kilometers. How long would it take a rocket, traveling at 3, point, 3, 5, times, 10, to the power 43.35×10
4
kilometers per hour to travel from Earth to Mercury? Round your answer to the nearest whole number of hours.
Answer
Attempt 1 out of 2

Answer:
hours

We can calculate the time required for the rocket to travel from Earth to Mercury using the formula:

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

We are given the following:

- Distance from Earth to Mercury: \( 9.21 \times 10^7 \) kilometers
- Speed of the rocket: \( 3.35 \times 10^4 \) kilometers per hour

### Step 1: Write down the formula
\[
\text{Time} = \frac{9.21 \times 10^7}{3.35 \times 10^4}
\]

### Step 2: Simplify the expression
To simplify the division of powers of 10, we subtract the exponents:
\[
9.21 \times 10^7 \div 3.35 \times 10^4 = \frac{9.21}{3.35} \times 10^{7 - 4} = \frac{9.21}{3.35} \times 10^3
\]

Now calculate \( \frac{9.21}{3.35} \):
\[
\frac{9.21}{3.35} \approx 2.75
\]

### Step 3: Calculate the final value
\[
\text{Time} = 2.75 \times 10^3 = 2750 \text{ hours}
\]

### Final Answer:
It would take approximately **2,750 hours** for the rocket to travel from Earth to Mercury.

---

Do you need any further details or explanations on this? Here are five related questions:

1. How would the time change if the rocket's speed increased by 20%?
2. What is the time in days instead of hours?
3. How is scientific notation helpful in this kind of calculation?
4. Can you calculate the time for a different distance, like Earth to Mars?
5. How would we adjust for the elliptical orbit of Mercury?

**Tip:** When using scientific notation, subtract the powers of 10 when dividing quantities.

The distance from Earth to Mercury is 9.21×10^7 kilometers. How long would it take a rocket, traveling at 3.35×10^4 kilometers per hour to travel from Earth to Mercury? Round your answer to the nearest whole number of hours.

Learn how to calculate the time it would take a rocket traveling at 3.35×10^4 km/h to reach Mercury from Earth, a distance of 9.21×10^7 kilometers. This problem covers scientific notation and the laws of exponents, making it ideal for students in Grades 8-10.

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