- Case Study - 1. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes, as shown in the figure. A competitor starts from the bucket, picks up the nearest potato, runs back to the bucket to drop it in, then returns to pick up the next potato. This process continues until all the potatoes are in the bucket. (i) What is the distance covered to pick up the first potato and drop it in bucket ?
- Case Study - 1. In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato. The other potatoes are arranged 3 m apart in a straight line, with a total of 10 potatoes, as shown in the figure. A competitor starts from the bucket, picks up the nearest potato, runs back to the bucket to drop it in, then returns to pick up the next potato. This process continues until all the potatoes are in the bucket. (i) What is the distance covered to pick up the first potato and drop it in bucket ?
10 m — the competitor runs 5 m to the potato and 5 m back to the bucket.
Marking Scheme
- 11 mark: correctly recognising the round trip (to the potato and back) and computing m.
- 2Acceptable working: stating distance = m earns full marks; answering 5 m (one way only) earns 0.
Hint
The competitor must run to the potato and back to the bucket, so double the 5 m distance.
Quick Oral Answer
Since the competitor runs to the first potato 5 m away and back to the bucket, the distance is metres, which is the first term of the AP for this race.
Analysis & Explanation
The opening part of the potato-race case study, establishing the first term of the underlying arithmetic progression.
Concept
- Each potato's distance is a round trip: out from the bucket to the potato, and back to drop it in.
- The first potato is 5 m away, so the round-trip distance = m — this becomes the first term () of the AP that governs the rest of the case study (common difference , since each potato is 3 m further, adding per trip).
Common Mistakes
- Recording only the one-way distance (5 m) and forgetting the return leg to the bucket.
Real-World Relevance
- This exact potato-race scenario (from NCERT) illustrates how arithmetic progressions model repeated, evenly spaced physical activity, such as a competitor's total running distance growing in a fixed pattern.
Common Mistakes
- 1Writing 5 m (only the one-way distance to the potato) and forgetting the return trip back to the bucket.
- 2Confusing the 3 m spacing between potatoes with the first potato's distance; the first potato is 5 m from the bucket, not 3 m.
- 3Attempting to apply the AP nth-term formula prematurely instead of simply doubling the given 5 m for the first potato.
Interesting Facts
This potato-race scenario is a well-known NCERT example: the round-trip distances form the AP 10, 16, 22, 28, … with first term 10 m and common difference 6 m, and the total distance for all 10 potatoes works out to 370 m.
The common difference is 6 m (not 3 m) precisely because every extra 3 m of spacing is travelled twice — once going and once returning — a neat illustration of how the physical setup doubles into the AP.
Potato races have been part of school sports days and fairs since the 19th century, and this problem shows how a simple playground game hides a clean arithmetic-progression pattern.
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Frequently Asked Questions
Why is the distance 10 m and not 5 m?
The competitor does not just run to the potato — they must pick it up and run back to the bucket to drop it in. So the trip is 5 m to reach the potato plus 5 m to return, giving m. Answering 5 m ignores the return leg and is incorrect.
How does this first distance connect to the rest of the case study?
This 10 m is the first term (a) of an arithmetic progression. Each next potato is 3 m further, so each round trip increases by m (the common difference d). The distances form the AP 10, 16, 22, 28, …, which is used in the later parts to find the nth-term distance and the total distance run.
Why is the common difference 6 m and not 3 m?
Although consecutive potatoes are 3 m apart, the competitor travels that extra 3 m twice — once running out to the potato and once running back to the bucket. So each round-trip distance grows by m, making the common difference of the AP equal to 6 m.