A signal from a spacecraft orbiting Mars travels to Earth at a speed of \( 3\times 10^8 \) meters per second. If the distance between Earth and the spacecraft is \(6.021 \times 10^8 \) kilometers, which of the following is closest to the number of minutes it will take for a signal from the spacecraft to reach Earth?

(1 kilometer = 1,000 meters)

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We can use the general rate equation, but we need to make sure to use the correct units. Since we want to obtain the number of minutes, we need to convert seconds into minutes. For the length, we can use either kilometers or meters as long as its consistent.

$$ d=6.021 \times 10^8 \text{ km} \cdot \frac{1{,}000 \text{ m}}{1 \text{ km}} $$ $$ d = 6.021 \times 10^{11} \text{ m} $$ $$ r = \frac{3 \times 10^8 \text{ meters}}{1 \text{ second}} \cdot \frac{60 \text{ seconds}}{1 \text{ minute}} $$ $$ r=1.8 \times 10^{10} \text{ m/min } $$

We are looking for time:

$$ d=rt $$ $$ t=\frac{d}{r} $$ $$ t=\frac{6.021 \times 10^{11} \text{ m}}{1.8 \times 10^{10} \text{ m/min }} $$ $$ \approx \boxed{33 \text{ min}} $$