Question

Question
An asteroid is heading toward Mars at the rate of 7.7×104
mi./hr. If the asteroid is 3.311×108
miles away from Mars, how many hours will it be before it hits Mars? Write the answer in scientific notation, expressed to the exact decimal place.(1 point)
hours

Answer 1

To find the time in hours it will take for the asteroid to hit Mars, you can use the formula:

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

Given:
- Distance = \(3.311 \times 10^8\) miles
- Speed = \(7.7 \times 10^4\) mi/hr

Now, substitute the values into the formula:

\[
\text{Time} = \frac{3.311 \times 10^8 \text{ miles}}{7.7 \times 10^4 \text{ mi/hr}}
\]

Calculating the division of the coefficients:

\[
\frac{3.311}{7.7} \approx 0.430
\]

Now, divide the powers of ten:

\[
\frac{10^8}{10^4} = 10^{8-4} = 10^4
\]

So, we have:

\[
\text{Time} \approx 0.430 \times 10^4 = 4.30 \times 10^3 \text{ hours}
\]

Therefore, the time before the asteroid hits Mars is:

\[
\boxed{4.30 \times 10^3 \text{ hours}}
\]