Question

Hii i'm stuck on this question

Answer 1

0. The neighbor's fencing project that will take the least amount of time to complete is ,Neighbor B.

,

1. The neighbor's fencing project that will take the most amount of time to complete is, Neighbor C.

Step-by-step explanation

Data given of Neighbor A

• Rectangular backyard.

• Can put up three 8-foot sections of wood fencing in two hours.

Data given of Neighbor B

• Circular fence.

,

• Can put up 15 ft of chain link fence per hour.

Data given of Neighbor C

• Fence around the three sides of his front yard.

,

• Can put up 1 yard of vinyl fencing in half an hour.

Procedure

We have to get the perimeter of the figures to evaluate how much time it will take to cover each fence.

• Neighbor A

Assuming that the fence will not cover the limit between the house and the backyard, then we can add the measures given per side:

`5+8+25+8=46ft`

As we are told that neighbor A can put up three 8-foot sections of wood fencing in two hours, neighbor A will take 5.75h in building the whole fence:

`46ft*(2h)/(8ft)=11.5h`

• Neighbor B

In this case, we have to add the diameter of the pool to the space between the pool and the fence, as it will be the diameter of the fence (df):

`d_f=30+5=35ft`

Then, the perimeter is:

`\pi d=\pi(35)`
`=35\pi ft`

Calculating the time it will take:

`35\pi ft*(1h)/(15ft)\approx7.33h`

• Neighbor C

Finally, the perimeter that will cover the fence for neighbor C is:

`16+58+16=90ft`

Calculating the time it will take:

`90ft*(0.5h)/(1ft)=45h`

Then:

• Neighbor A will take 11.5h.

,

• Neighbor B will take 7.33h

,

• Neighbor C will take 45h.