Mars Days

Number Theory Level 2

A day on Mars is roughly 24 hours and 40 minutes long.

Using this estimate, after 100 days on Mars pass, how many full days on Earth will have passed? (The time will end on an Earth day that is only part of the way through; ignore that day.)


The answer is 102.

Jason Dyer by Jason Dyer

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3 solutions

Jason Dyer Staff
Jan 11, 2017

After 3 Mars days, Mars has an extra 40 × 3 = 120 40 \times 3 = 120 minutes or 2 hours more pass compared to Earth. Since there are 12 sets of 2 hour segments in a day, every 3 × 12 = 36 3 \times 12 = 36 days one extra Earth day passes compared to Mars.

Rounding down, after 100 Mars days Earth will have 100 / 36 100 / 36 or 2 full days more than Mars, so Earth has 100 + 2 = 102 100 + 2 = 102 days pass.

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Zach Abueg
Jan 10, 2017

40 40 minutes ÷ ÷ 60 60 minutes in an hour ≈ 0.66 ≈ 0.66 hours

24.66 24.66 hours × 100 ≈ 2466 \times 100 ≈ 2466 hours

2466 2466 hours ÷ ÷ 24 24 hours in a day ≈ 102.75 ≈ 102.75 days

Because it asks for number of full days, the answer is 102. 102.

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Elijah Frank
Dec 26, 2020

40/60 = 0.66... is 100*0.66= 66/24=2.75 Days more

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