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In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and 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?[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2×5+2×(5+3)]
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and 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?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2×5+2×(5+3)]
Arithmetic Progression | CBSE | Class 10 | Maths | NCERT
In a potato race, a bucket is placed at the starting point, which is 5 m from the first potato and 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?
[Hint: to pick up the first potato and the second potato, the total distance (in metres) run by a competitor is 2×5+2×(5+3)]

Solution:

The distances between the bucket and the potatoes are 5, 8, 11, 14,…, which is in the form of AP.

Given that the competitor’s journey for gathering these potatoes is two times the distance at which the potatoes were kept,

Distances to be run w.r.t distances of potatoes, could also be written as;

10, 16, 22, 28, 34,……….

As a result, the first term, a = 10 and d = 16−10 = 6

S10 =?

Using the formula of sum of n terms, we know,

${{S}_{10}}=\frac{12}{2}\left[ 2\left( 20 \right)+\left( n-1 \right)\left( -1 \right) \right]$

= 5[20+54]

= 5(74)

= 370

As a result, the competitor will cover a total distance of 370 metres.

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