# 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 10 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 he continues in the same way until all the potatoes are in the bucket. What is the total distance the competitor has to run?

To pick the first potato, the competitor has to run 5 m to reach the potato and 5 m to run back to the bucket.

Total distance covered by the competitor to pick first potato = 2 × (5) = 10 m

To pick the second potato, the competitor has to run (5 + 3) m to reach the potato and (5 + 3) m to run back to the bucket.

Total distance covered by the competitor to pick second potato = 2 × (5 + 3) = 16 m

To pick the third potato, the competitor has to run (5 + 3 + 3) m to reach the potato and (5 + 3 + 3) m to run back to the bucket.

Total distance covered by the competitor to pick third potato = 2 × (5 + 3 + 3) = 22 m

This will continue and we will get a sequence of distance as 10, 16, 22,… upto 10 terms (as there are 10 potatoes to pick).

Total distance covered by the competitor to pick all the 10 potatoes = 10 + 16 + 22 + … upto 10 terms.

This forms an Arithmetic series with first term = a = 10

and Common difference = d = 6

Number of terms = n = 10

Now, S10 = (10/2)[2a + (10 - 1)d]

= 5 × [2(10) + 9(6)]

= 5 × [20 + 54]

= 5 × 74

= 370

Total distance covered by the competitor = 370 m

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