In a children potato race, n potatoes are placed I metre apart in a straight line A competitor sarts from a point in the line which is 5 metre from the nearest potato. Find an expression for the total distance run in collecting the potatoes, one at a time and bringing them back one at a time to the starting point. Calculate the value of 'n if the total distance run is 162 metres.
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Step-by-step explanation:
The distances of potatoes from the bucket are 5,8,11,14…
Distance run by the competitor for collecting these potatoes are two times of the distance at which the potatoes have been kept. Therefore, distances to be run are
10,16,22,28,34,……….
a=10,d=16−10=6
To find: S10
S10=210[2(10)+(10−1)6]
=5[20+54]
=5(74)
=370
Therefore, the competitor will run a total distance of 370 m.
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