Question

The students of a school decided to beautify the school on an annual day by fixing colorful 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 in 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. What is the maximum distance she traveled carrying a flag?

Answer 1

As the total number of flags is 27, so there would be 13 flags on one side, 13 flags on the other side and one flag in the middle.

Consider that she fixes 13 flags on one side of the middle flag.

So, the distance covered by Ruchi to fix the first flag and return is $2m+2m=4m$.

The distance covered by Ruchi to fix the second flag and return is $4m+4m=8m$.

Similarly, the distance covered by Ruchi to fix the thirteenth flag and return is $4m+8m+12m\cdots +13terms$.

It will form an arithmetic series,

$4m+8m+12m\cdots +13terms$

$=\frac{13}{2}\left[2\left(4\right)+\left(13-1\right)4\right]$

$=\frac{13}{2}\left(56\right)$

$=364m$

The total distance travelled by Ruchi to fix the flags and return back is $2\times 364=728m$.

The total distance covered by Ruchi only to carry the flag is $\frac{1}{2}\times 728=364m$.