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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 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 × 5 + 2 × (5 + 3)]
Asked by Aamir Last Modified
Answer 
Sherine Das
Well Qualified and Certified Mathematics B.Ed(M.G Usty)Teacher with more than13 years of Experience
Distance ran by him one way to complete the race=5+(5+3)+(5+3+3)+(5+3+3+3)+(5+3+...9tim) =5+8+11+14+.....+32,which is in arithmetic progression;
first term;a=5,common difference;d=8-5=3&nth term is an=32. Sn=n/2[2a+(n-1)d]
Sum to n- terms = 10/2[10+(10-1)3] = 5[10+27]=5x37=185;but he completes his run to and fro,so multiply 185 by 2=370m.
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The competitor has to cover the same distance twice,
Here a=5 d=3 and l=a10 =5+9*3=5+27=32
Total distance covered by the competitor=2[(10/2)(5+32)]
=2(5*37)=2*185=370m
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