Cleaning time!
Mai and Mio decided to earn some money by cleaning a local warehouse. Inside area of the warehouse is 36 thousands square units (as shown in the image above , shape of warehouse from the bird perspective is similar to a rectangle with sides of 180 and 200 units).
Here is the plan: Mai and Mio will start cleaning from points (red point) and (blue point), respectively, each one will be heading down and when wall is reached, Mai will go one square unit right and Mio one left , ater that, both will go up . When wall is reached, Mai goes right , Mio left , and both will go down again and so on, until they clean the warehouse.
Mai will clean 11 , whilst Mio, for the same time, will clean 7 square units. At the moment when work is finished, how many square units will be between Mai and the wall marked (a square unit on which Mai will be standing in that moment is not included in that number)?
The answer is 140.
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1 solution
Solution:
Whole warehouse is 7 k + 1 1 k = 1 8 k = 3 6 0 0 0 . k = 2 0 0 0 , which means Mai will be cleaning 1 1 k = 2 2 0 0 0 .
2 2 0 0 0 = 1 2 2 × 1 8 0 + 4 0 (180 is number of square units she needs to clean before changing her "up/down" course). On odd numbered column (1st, 3rd, 5th ...) she will be heading down, while on even numbered she will be heading up. After 122nd (which would then be up), she will start 123rd column and will clean 40 square units, before "bumping into" Mio. Therefore, she will be 39 square units away from "starting wall" ( C D ), will be standing on 40th square unit, and will be 140 square units distanced from A B wall.
Therefore, solution is 1 4 0 .