Question 452 marksSection E

  1. (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.

Arithmetic Progressions
Sum of an AP applied to speed-time

Official answer

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

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

Marking scheme

  1. 1.1 mark: correct use of the relation Time=Total distance÷Speed\text{Time} = \text{Total distance} \div \text{Speed} with the total distance 370 m and speed 5 m/s substituted.
  2. 2.1 mark: correct final answer 74 seconds (accept 1 min 14 s).
  3. 3.Follow-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 time=distance÷speed\text{time} = \text{distance} \div \text{speed}.

Quick oral answer

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

Common mistakes

  1. 1.Multiplying distance by speed (370×5370 \times 5) instead of dividing, giving an incorrect and unrealistic value.
  2. 2.Carrying forward a wrong total distance from part (a), such as using 64 m or 185 m instead of 370 m.
  3. 3.Leaving the answer in minutes wrongly (e.g., 74 minutes) — the unit is seconds since speed is in metres per second.

Analysis and explanation

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


Concept

  • Time=Total distance÷Average speed\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.
  • Time=370÷5=74\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.

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.

Question details

Q45 of 53 questions

Board
CBSE
Class
Class 10
Subject
Mathematics (Basic)
Year
2026
Section
Section E
Marks
2
Chapter
Arithmetic Progressions
Topic
Sum of an AP applied to speed-time
Bloom's level
apply
Syllabus topic
Unit 2: Algebra — Arithmetic Progressions: Sum of an AP combined with speed-distance-time (CBSE Class 10 Mathematics)
Author
CBSE
Reviewed by
Padhantu Academic Team

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Frequently asked questions

Which formula connects distance, speed and time?

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