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

Arithmetic Progressions

Arithmetic Progressions - Application (Potato Race)

Official Answer

16 m — the second potato is $5 + 3 = 8\text{ m}$ from the bucket, so the round trip is $8 + 8 = 16\text{ m}$ .

potato racesecond potatoarithmetic progressioncommon differenceround trip distance

Marking Scheme

11 mark: correct final answer of 16 m, showing the distance 8 m to the potato doubled for the return trip.

Hint

Second potato is $5 + 3 = 8\text{ m}$ from the bucket; double it for the round trip.

Quick Oral Answer

The second potato is 8 m from the bucket (5 m + 3 m gap), so the round trip is $8 + 8 = 16\text{ m}$ .

Checks whether the 3 m gap between potatoes is correctly added before doubling for the return trip, revealing the AP's common difference.

Concept

Second potato lies 3 m further than the first, so its one-way distance is $5 + 3 = 8\text{ m}$ ; the round trip doubles this.
Comparing 16 m (2nd potato) to 10 m (1st potato) gives common difference $d = 6\text{ m}$ , since the 3 m gap is doubled on both legs.

Key Points

Common Mistakes

Adding the 3 m gap only once instead of accounting for both the outward and return legs.
Confusing the one-way gap (3 m) with the round-trip common difference (6 m).

1Forgetting to add the 3 m gap between the first and second potato before doubling.
2Doubling only the gap (3 m) instead of the full distance from the bucket (8 m).

The pattern of round-trip distances ( $10, 16, 22, \ldots$ ) forms an AP with common difference 6 m — exactly twice the 3 m gap between potatoes.

This kind of 'shuttle run' distance problem is also used in physical education research to estimate athlete fatigue over repeated sprints.

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6 m, since each potato is 3 m farther than the previous one and the distance is doubled for the round trip ( $2 \times 3 = 6$ ).