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?

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 = $\dfrac{n}{2}$[2a + (n - 1)d]

S₁₀ = $\dfrac{10}{2}$[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.