Question

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 2.5 years
about 22.5 years
about 1 year
about 7.5 years

Explanation:

Step1: Find time to Mars in days

Since Mars is 140 times farther than the moon, and time to moon is 3 days, time to Mars (in days) is \( 3\times140 = 420 \) days.

Step2: Convert days to years

There are about 365 days in a year. So, \( \frac{420}{365}\approx1.15 \) years, which is about 1 year. Wait, no, wait—wait, maybe I miscalculated. Wait, 3 days to moon, Mars is 140 times farther. So time is 3140 = 420 days. 420/365 ≈ 1.15, but wait, maybe the options—wait, maybe I made a mistake. Wait, no, let's check again. Wait, 3 days for moon. Mars is 140 times farther. So time is 3140 = 420 days. 420 days is about 1.15 years, which is about 1 year? But wait, maybe the question is different. Wait, no, maybe I messed up. Wait, no, let's recalculate. 3 days 140 = 420 days. 420 / 365 ≈ 1.15, so about 1 year. But wait, the options have about 1 year. Wait, but maybe my approach is wrong? Wait, no, in a simple model, time is proportional to distance (if speed is constant). So speed to moon: distance / time = 386400 km / 3 days = 128800 km/day. Distance to Mars: 386400 140 = 54096000 km. Time to Mars: 54096000 / 128800 = 420 days. 420 days is about 1.15 years, so about 1 year. So the correct option is about 1 year. Wait, but let me check the options again. The options are about 2.5, 22.5, 1, 7.5. So 420 days is about 1 year (since 365 days is a year, 420 is ~1.15, so about 1 year). So the answer is about 1 year.

Answer:

about 1 year