What is the distance covered to pick up the first potato and drop it in bucket ?

Arithmetic Progressions

Arithmetic Progressions - Application (Potato Race)

Official Answer

10 m — the competitor covers 5 m to reach the first potato and 5 m to return and drop it in the bucket, giving a round trip of $5 + 5 = 10\text{ m}$ .

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Marking Scheme

11 mark: correct final answer of 10 m, with the reasoning that the distance is doubled (5 m to reach + 5 m to return).

Hint

Remember the competitor runs to the potato AND back to the bucket — always double the one-way distance.

Quick Oral Answer

The first potato is 5 m from the bucket, so the competitor runs 5 m to pick it up and 5 m back to drop it — a total of 10 m.

Analysis & Explanation

Tests converting a 'pick up and drop' instruction into a round-trip distance — the seed value of the potato-race AP.

Concept

The competitor must run to the potato AND back to the bucket, so the distance is doubled, not one-way.
This round trip becomes the first term (a = 10 m) of the AP used for all later parts of the case study.

Key Points

First potato is 5 m from the bucket ⇒ one-way = 5 m.
Round trip = $5\text{ m} + 5\text{ m} = 10\text{ m}$ .

Common Mistakes

Writing only 5 m (one-way) and ignoring the return trip implied by 'drop it in bucket'.
Forgetting this value seeds a = 10 for the AP needed in the following sub-questions.

Common Mistakes

1Writing only 5 m (one-way distance) and forgetting the return trip to the bucket.
2Confusing this with the distance to the second potato instead of the first.

Interesting Facts

This potato race problem is one of the most famous application-based examples of Arithmetic Progressions in the NCERT Class 10 Mathematics textbook (Chapter 5).

Potato races are a real event in school sports days in India, and the mathematics of the total distance run is a classic example of how AP models real athletic events.

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Frequently Asked Questions

Why is the distance for the first potato doubled?

Because the competitor must run from the bucket to the potato (5 m) and then run back to the bucket to drop it (another 5 m), making a round trip of 10 m.

How does this relate to Arithmetic Progressions?

The round-trip distance for each potato forms an AP: $10, 16, 22, \ldots$ with first term 10 m and common difference 6 m, since each subsequent potato is 3 m farther, doubling to 6 m more per round trip.