What is the maximum distance she travelled carrying a flag ?

Question

 The students of a school decided to beautify the school on the Annual Day by fixing colourful flags on the straight passage of the school. They have 27 flags to be fixed at intervals of every 2 m. The flags are stored at the position of the middle most flag. Ruchi was given the responsibility of placing the flags. Ruchi kept her books where the flags were stored. She could carry only one flag at a time. How much distance did she cover in completing this job and returning back to collect her books ? What is the maximum distance she travelled carrying a flag ?

now in the total question explain me the last part of the question.i'e. What is the maximum distance she travelled carrying a flag ?

question belongs to arithmatic progressions class x 

Answer 1

The central flag is 14. The first flag and the last flag are each a distance 26m away. After placing flag 1 and flag 27 in place she has to return to flag 14 to pick up the next pair of flags (flags 2 and 26). This means that the distance she covers is 26m (to flag 1)+26m (back to flag 14)+26m (to flag 27)+26m (back to flag 14)=104m.

Then she places flags 2 and 26 so the distance is 4*24m=96m.

Flags 3 and 25, distance=4*22=88m; ...flags 13 and 15, distance=4*2=8m.

This gives us the sum: 104+96+88+...+8=8(13+12+11+...+1)=8*13*14/2=728m.

The greatest distance she has to walk is to place flag 1 or flag 27=2*26=52m.

Fixing flag 14 doesn’t require her to go any distance at all.

Comments

yes ur right i thought the way u had .the ans is 52mtrs. only, but answer given is  26 mtrs.how that is possible .can u please check it

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Yes, I included the walk back but the question only asks how far she walked carrying the flag, so the answer is 26m. she walked back without the flag, of course!

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i am confused on this answer becoz from 14 to 1 flags distance is 26 mtrs . by carrying a flag,then she has to walk to the other side again 14 to 27,which is again 26 mtrs. .so the maximum distance must be 52 only.i think answer given is wrong .what do u say on this point

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She walks 26m from flag 14 to flag 1. She fixes the flag and walks back to pick up the next flag, another 26m. She picks up flag 27 and walks 26m to put it in place. Then she returns to flag 14 to pick up flag 2. So she has walked 104m to place flags 1 and 27.

The next two flags would be 2 and 26 which are both 24m away so she has to cover 96m to place these. The series is 104+96+88 and so on until she has only 8m to walk to fix flags 13 and 15. She then puts flag 14 in place, picks up her things and leaves.

So she walks half the distance carrying flags to their destinations and half the distance empty-handed walking back to flag 14 after placing the flags.

Does that make sense?