Question

Kiteretsuki builds a robot to help him paint a fence. The robot has a paint roller of width 1 foot, that works like a ball-point pen, so it has a steady flow of ink. Kiteretsuki sets the robot to work and leaves but doesn't realize that the robot has a programming error.
It paints one foot of the fence from left to right, then stops and paints a foot in the right to left direction. It then starts moving from left to right again, but this time moving two feet instead of one. However, after this, it only moves back to its previous position. The robot carries on in this fashion, increasing its reach by 1 foot every left to right movement and then returning to its previous starting point.
If Kiteretsuki returns after the robot have moved a total of 11 times, how many inches of the fence has the robot painted in that time?​

Answer 1

Given : The robot has a paint roller of width 1 foot,

It paints one foot of the fence from left to right, then stops and paints a foot in the right to left direction. It then starts moving from left to right again, but this time moving two feet instead of one. However, after this, it only moves back to its previous position.

. The robot carries on in this fashion, increasing its reach by 1 foot every left to right movement and then returning to its previous starting point.

To Find : how many inches of the fence has the robot painted in that time?​

Solution:

Robot moves 1 st time  - Paint 1 feet

Robot goes back in 2nd time hence - that 1 feet is painted again

Robot moves 2 feet in 3rd time - Hence paint  2 feet  ( 1 feet was already painted )

Robot goes back in 4th time hence - that 2 feet is painted again

Robot moves 3 feet in 5th time - Hence paint  3 feet  ( 2 feet was already painted )

Robot goes back in 6th time hence - that 3 feet is painted again

and so on

4 feet in 7th and 8th

5 feet in 9th and 10th

6 feet in 11th

Hence 6 feet of fence is painted in length

1 feet = 12 inches

Hence 6 * 12 = 72 inches fence painted  in length

And roller width is  1 foot  = 12 inches

Total fence painted = 72 x 12 = 864 sq inches fence painted. in area

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