To find out how long it would take the spacecraft to reach Mars, we can use the information given about the distance to the Moon and the relative distance to Mars.
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The distance from Earth to the Moon is about 386,400 km.
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Mars is about 140 times farther away than the Moon, which means the distance from Earth to Mars is approximately: \[ 386,400 , \text{km} \times 140 \approx 54,096,000 , \text{km}. \]
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The spaceship takes 3 days to cover the distance to the Moon. To find the speed of the spaceship, we can calculate the speed as follows:
- Distance to the Moon: 386,400 km
- Time taken to Moon: 3 days = 3 × 24 = 72 hours.
- Speed = Distance / Time = \( \frac{386,400 , \text{km}}{72 , \text{hours}} \approx 5,366.67 , \text{km/h}. \)
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Now we'll calculate the time it would take to reach Mars using the same speed:
- Distance to Mars: 54,096,000 km
- Time = Distance / Speed = \( \frac{54,096,000 , \text{km}}{5,366.67 , \text{km/h}} \approx 10,100 , \text{hours}. \)
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To convert hours to years:
- Number of hours in a year = 24 hours/day × 365 days/year = 8,760 hours/year.
- Time in years = \( \frac{10,100 , \text{hours}}{8,760 , \text{hours/year}} \approx 1.15 , \text{years}. \)
So, the spaceship would take about 1 year to reach Mars.
The correct answer is about 1 year.
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