Question

You are having a family meeting during the a epidemic. You want to follow the guidelines and know everyone has to stay 6 feet apart?

a. If your room has an area of 288 square feet (12 x 24) how many people can you invite?

b. You get to your meeting and you find out the meeting space is occupied. You search for another room and you locate one which has the same area, 288 square feet, but is (16 x 18) instead. If you have to remain 6 feet apart, can you fit the same amount of people into both rooms?

Answer 1

a. 15 people

b. You cannot fit the same amount of people

Explanation:

In this problem, the space occupied by each person will be neglected, that is, people will be treated as "points"

a. The distance between consecutive people horizontally and vertically has to be 6 feet.

In 12 feet, the 6 ft distance can be taken twice, which means that each horizontal row can have three people.

In 24 feet, the 6 ft distance can be taken four times, which means that each vertical row can have five people.

The number of people you can invite is:

`n=3*5\\n=15\ people`

b. In 16 feet, the 6 ft distance can be taken twice (4 ft of dead space), which means that each horizontal row can have three people.

In 18 feet, the 6 ft distance can be taken three times, which means that each vertical row can have four people.

The number of people you can invite is:

`n=3*4\\n=12\ people`

Therefore, you cannot fit the same amount of people.

Answer 2

a.

Total No. of People = 8 people

b.

Total No. of People = 6 people

Hence, we can not fit the same amount of people in both rooms.

Explanation:

a.

Here, the dimensions of the room are 12 ft by 24 ft. So, in order to maintain the 6 ft distance, we can allow following number of people in it.

No. of people along 24 ft dimension = 24 ft/6 ft

No. of people along 24 ft dimension = 4

No. of rows along 12 ft dimension = 12 ft/6 ft

No. of rows along 12 ft dimension = 2

So, the total no. of people is given as:

Total No. of People = (People along 24 ft)(Rows along 12 ft)

Total No. of People = (4)(2)

Total No. of People = 8 people

b.

Here, the dimensions of the room are 16 ft by 18 ft. So, in order to maintain the 6 ft distance, we can allow following number of people in it.

No. of people along 16 ft dimension = 16 ft/6 ft

No. of people along 16 ft dimension = 2.67

In order to maintain minimum 6 ft distance the no. of people is rounded down to 2.

No. of people along 16 ft dimension = 2

No. of rows along 18 ft dimension = 18 ft/6 ft

No. of rows along 18 ft dimension = 3

So, the total no. of people is given as:

Total No. of People = (People along 24 ft)(Rows along 12 ft)

Total No. of People = (2)(3)

Total No. of People = 6 people

Hence, we can not fit the same amount of people in both rooms.