(iii) (b) If average speed of competitor is 5 m/s, then find the average time taken by competitor to put all the potatoes in the bucket.

Q: Which formula connects distance, speed and time?

$\text{Time} = \text{Distance} \div \text{Speed}$. Here $\text{time} = 370\text{ m} \div 5\text{ m/s} = 74\text{ seconds}$.

Arithmetic Progressions

Sum of an AP applied to speed-time

Official Answer

74 seconds (1 minute 14 seconds). Using $\text{Time} = \text{Total distance} \div \text{Speed} = 370\text{ m} \div 5\text{ m/s} = 74\text{ s}$ .

74 secondstime = distance/speed370 m5 m/saverage time370 ÷ 51 min 14 sspeed distance time

Marking Scheme

11 mark: correct use of the relation $\text{Time} = \text{Total distance} \div \text{Speed}$ with the total distance 370 m and speed 5 m/s substituted.
21 mark: correct final answer 74 seconds (accept 1 min 14 s).
3Follow-through (error-carried-forward) credit if the student divides their own total distance from part (a) correctly by 5.

Hint

Take the total distance from part (a) — 370 m — and divide by the speed 5 m/s using $\text{time} = \text{distance} \div \text{speed}$ .

Quick Oral Answer

The total distance is 370 m and the speed is 5 m/s, so $\text{time} = 370 \div 5 = 74$ seconds, which is 1 minute 14 seconds.

Analysis & Explanation

This part links the AP total from part (a) to a simple kinematics relation.

Concept

$\text{Time} = \text{Total distance} \div \text{Average speed}$ , using the 370 m found in part (iii)(a) and the given speed of 5 m/s.
$\text{Time} = 370 \div 5 = 74$ seconds (= 1 minute 14 seconds).

Key points

Follow-through (error-carried-forward) credit applies: if the total distance in part (a) was wrong but the division here is done correctly, the mark for this part is still awarded.

Common mistakes (परीक्षा में सावधानी)

Multiplying distance and speed instead of dividing, which gives a meaningless 1850.

Real-world

The same distance ÷ speed chain is used to time repeated equal-step journeys such as delivery rounds or machine strokes run at a steady pace.

Common Mistakes

1Multiplying distance by speed ( $370 \times 5$ ) instead of dividing, giving an incorrect and unrealistic value.
2Carrying forward a wrong total distance from part (a), such as using 64 m or 185 m instead of 370 m.
3Leaving the answer in minutes wrongly (e.g., 74 minutes) — the unit is seconds since speed is in metres per second.

Interesting Facts

At 5 m/s (18 km/h) the competitor moves at roughly the pace of a brisk recreational jog, so 370 m in 74 s is a realistic field-event figure.

74 seconds is exactly 1 minute 14 seconds, a neat conversion that examiners often accept as an alternative form.

Because the trips lengthen steadily, the competitor is slowest-progressing at the end — real racers pace themselves knowing the last potato is the farthest.

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Frequently Asked Questions

Which formula connects distance, speed and time?

$\text{Time} = \text{Distance} \div \text{Speed}$ . Here $\text{time} = 370\text{ m} \div 5\text{ m/s} = 74\text{ seconds}$ .

Where does 370 m come from?

It is the total distance from part (iii)(a), found by summing the AP of to-and-fro distances for all ten potatoes.

Can the answer be written in minutes?

Yes, 74 seconds equals 1 minute 14 seconds; both forms are acceptable.