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 (see Fig.) 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?
[Hint:To pick up the first potato and the second potato, the total distance (in metres) run by a competitor is $2 \times 5 + 2 \times (5 + 3)]$

Given:

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.

To do:

We have to find the total distance the competitor has to run.

Solution:

Distance between the first potato and the bucket $= 5\ m$

Distance between the next 2 potatoes $= 3\ m$

The distances form a series of $5\ m, 8\ m, 11\ m,.....$

Here,

$a = 5, d = 8 - 5= 3$

Therefore,

Total distance travelled for 10 potatoes $= 2 [5 + 8 + 11 + …….. + 10\ terms]$

$= 2[\frac{10}{2}{2(5)+ (10 - 1) 3}]$             (Since $S_n=\frac{n}{2}[2a+(n-1)d]$)

$= 2[5{10 + 27}]$

$= 2[5(37)]$

$= 37 \times 10$

$= 370$

The total distance the competitor has to run is 370 m.

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Updated on: 10-Oct-2022

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