Question

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. 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?
(ii) What is the distance covered to pick up the second potato and drop it in bucket?
(iii) (a) What is the total distance the competitor has to run? OR
(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.}

Hint:

Always remember to double the distance in "back and forth" problems; the most common mistake is calculating the distance to the object only.

Answer 1

Step 1: Understanding the Pattern Clearly:
The potatoes are placed at equal distances from the bucket, forming an Arithmetic Progression (AP).
Distance of first potato from bucket = 5 m
Common difference between consecutive potatoes = 3 m

Since the competitor runs to the potato and comes back to the bucket, the actual distance covered for each potato is:
2 × (Distance from bucket)

So the running distances will also form an AP.

Step 2: Forming the Required AP:
Distance of 1st potato run = 2 × 5 = 10 m
Distance of 2nd potato run = 2 × 8 = 16 m
Distance of 3rd potato run = 2 × 11 = 22 m

Thus the sequence becomes:
10, 16, 22, 28, …

Here,
a = 10 (first term)
d = 6 (common difference)
n = 10 (number of potatoes)

Step 3: Total Distance Covered:
Using the sum formula of AP:
S_n = n/2 [2a + (n − 1)d]

S₁₀ = 10/2 [2(10) + (10 − 1)6]
= 5 [20 + 54]
= 5 × 74
= 370 m

Step 4: Time Taken (Alternative Part):
Speed = 5 m/s

Time = Total Distance / Speed
= 370 / 5
= 74 seconds

Final Answers:
(i) 10 m
(ii) 16 m
(iii)(a) 370 m
(iii)(b) 74 seconds