PLEASE SHOW ALL WORK AND EXPLAIN Picture above is a dramatiz

PLEASE SHOW ALL WORK AND EXPLAIN

Picture above is a dramatization of the problem and does not accurately depict the situation. The picture should only be used as an illustration of the idea behind the scenario. Below is an artist rendition. Scenario: There is a light rain, no wind, and the rain falls straight down. A 9ftX3ft tarp covers a 3ft wide sidewalk in front of a building entrance. The rain does not directly contact the sidewalk under the tarp and the ground is completely level. However, wet shoes leave wet footprints. Assume: the ground under the tarp can only get wet via footprints. the footprint is 1ftX3in, they wear rectangular shoes. the footprints never overlap, they are superstitious. they walk at a rate of 2ft per second they each leave 5 footprints as they pass under the tarp. each step leaves a wet print. The foot prints evaporate instantly after 20 minutes. There is a constant and evenly spaced flow of people under the tarp at a rate of 3 every 12 minutes After an hour what percentage of the walkway under the tarp is wet? If this scenario went on indefinitely what percentage of the ground under the tarp would be wet? What is the minimum rate (people/hour) for the entire walk way to be wet after one hour?

Solution

Solution : In an hour , the foot prints of first 40 minutes will disappear. The ground will wet due to only those foot prints which appear in last 20 minutes.

One people covers area when passing the ground 5*1*0.25=1.25 sq ft.

In 12 min 3 people passes, thus in 20 minutes 3*20/12 = 5 people.

Foot print of 5 people = 5*1.25 = 6.25 sq ft.

Total space under the trap = 9*3 =18 sq ft.

Thus in one hour the percentage wet area = 6.25*100/18 =34.72 %. Ans.

---------------------------------------------

If the scenario on indefinitely, then the percentage wet area will be same i. e. 34.72 %.

---------------------------------------------------------

In one hour, foot print of 5 people will be appear. Thus rate is 5 people /hour.