A human-operated spaceship reaches the moon in 3 days. The moon is about 386,400 km from Earth. Mars, our closest planetary neighbor, is, at its closest, about 140 times farther away from us than the moon if Mars stays in place. Assuming a very simple model of the solar system, about how long would it take that same spaceship to reach Mars?(1 point)

about 7.5 years

about 1 year

about 2.5 years

about 22.5 years

1 answer

To find the estimated time it would take for the spaceship to reach Mars, we can use the proportion based on the distance comparison between the moon and Mars:

Moon distance: 386,400 km
Mars distance: 140 times farther than the moon

So, Mars distance = 386,400 km * 140 = 54,096,000 km

Now, we can set up a proportion to find the time it would take to reach Mars:

Moon travel time: 3 days
Mars travel time: x days

Moon distance: 386,400 km
Mars distance: 54,096,000 km

The proportion is:

3 days / 386,400 km = x days / 54,096,000 km

Cross-multiplying and solving for x:

386,400 km * x days = 3 days * 54,096,000 km
386,400x = 162,288,000 days
x ≈ 162,288,000 days / 386,400

x ≈ 420.51 days

Therefore, it would take approximately 420.51 days (or about 1 year and 55.5 days) for the same spaceship to reach Mars. Therefore, the closest answer choice is about 1 year.