In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

Question

In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato, and the other potatoes are placed 3 m apart in a straight line. There are ten potatoes in the line.
A competitor starts from the bucket, picks up the nearest potato, runs back with it, drops it in the bucket, runs back to pick up the next potato, runs to the bucket to drop it in, and she continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

KnowledgeBoat · Accepted Answer

From figure, The distances of potatoes are : 5, 8, 11, 14, ... It can be observed that these distances are in A.P. First term (a) = 5 Common difference (d) = 8 - 5 = 3 Number of terms (n) = 10 By formula, S_n = [2a + (n - 1)d] S₁₀ = [2 × 5 + (10 - 1) × 3] = 5[10 + 27] = 5 × 37 = 185 Since, every time she has to run back to the bucket, therefore, the total distance that the competitor has to run will be two times the total distance = 2 × 185 m = 370 m. Hence, the competitor will run a total distance of 370 m.

Mathematics

AP

Related Questions

200 logs are stacked in the following manner: 20 logs in the bottom row, 19 in the next row, 18 in the row next to it and so on. In how many rows are the 200 logs placed and how many logs are in the top row?

Which term of the AP : 121, 117, 113,……, is its first negative term?

The sum of the third and the seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.