Problem 14 · 2017 Math Kangaroo
Medium
Algebra & Patterns
arithmetic-sequence
Paul goes on a 5-day hike, starting on Monday and finishing on Friday. Each day he walks 2 km more than the day before, and in total he walks 70 km. How far does he walk on Thursday?
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Answer: E — 16 km
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Hint 1 of 2
The five daily distances rise by 2 km each day, so they are evenly spaced around the middle day.
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Hint 2 of 2
The middle (Wednesday) distance is the average; find it, then step up to Thursday.
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Approach: use the average of an arithmetic sequence
- Five days increasing by 2 km average to the middle day, Wednesday: 70 ÷ 5 = 14 km.
- Each later day is 2 km more, so Thursday = 14 + 2 = 16 km.
- He covers 16 km on Thursday (E).
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