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. Based on the above information, answer the following questions :
Question: 1
What is the distance covered to pick up the first potato and drop it in bucket ?
Show Hint
Remember to double the distance for every potato because of the "to-and-fro" movement.
Step 1: Understand the Movement:
To collect one potato, the competitor runs from the bucket to the potato and then returns back to the bucket.
Hence, the total distance covered is twice the distance of the potato from the bucket.
Step 2: Given Distance:
Distance of the first potato from the bucket \( = 5 \text{ m} \).
Step 3: Calculate Total Distance Covered:
Distance to reach the potato \( = 5 \text{ m} \).
Distance to return to the bucket \( = 5 \text{ m} \).
Step 1: Understand the Pattern:
Each potato is placed 3 m farther from the bucket than the previous one.
So, the distances form an increasing pattern with a common difference of 3 m.
Step 2: Calculate the Distance of the Second Potato:
Distance of 1st potato from bucket \( = 5 \text{ m} \).
Distance of 2nd potato from bucket \( = 5 + 3 = 8 \text{ m} \).
Step 3: Find the Total Distance Covered:
The competitor runs to the potato and comes back to the bucket.
So, total distance for the 2nd potato:
\[
\text{Total distance} = 2 \times 8
\]
\[
\text{Total distance} = 16 \text{ m}
\]
Step 4: Final Answer:
\[
\boxed{\text{Distance covered for second potato} = 16 \text{ m}}
\]
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Question: 3
What is the total distance the competitor has to run ?
Show Hint
Alternatively, calculate the sum of distances to the potatoes \( \sum = (5 + 8 + 11 + \dots) \) and then double the final result.
Step 1: Identify the Pattern:
The distances form an Arithmetic Progression (AP) because each term increases by a fixed amount.
Step 2: Write the Given Values:
First term \( a = 10 \text{ m} \)
Second term \( = 16 \text{ m} \)
Common difference \( d = 16 - 10 = 6 \text{ m} \)
Number of terms \( n = 10 \)
Step 1: Recall the Basic Formula:
The time required to cover a certain distance is calculated using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Step 2: Note the Given Values:
Total distance covered \( = 370 \text{ m} \)
Average speed \( = 5 \text{ m/s} \)
