Question

It is reported that approximately 20 squaremiles of dry land and wetland were convertedto water along the Atlantic coast between 1996and 2011. A small unpopulated island in the AtlanticOcean is 2000 ft wide by 9,380 feet long. Atthis rate, how long before the island issubmerged?

Answer 1

2 months

1) Notice that the sinking rate is 20miles² per 5 years (2011-1996) so:

`(20)/(5)=(4m^2)/(y)`

So the rate is 4 square miles per year.

2) We need to convert those measures from feet to miles:

`\begin{gathered} 1\text{ mile=5280ft} \\ 2000ft=(2000)/(5280)=0.378miles \\ 9380ft=(9380)/(5280)=1.7765miles \end{gathered}`

So, now let's find the area multiplying the width by the height:

`\begin{gathered} A=1.7765\cdot0.378 \\ A=0.671517m^2 \end{gathered}`

Now, considering the sinking rate of 4miles²/year we can write the following pair of ratios:

`\begin{gathered} 1year-------4miles^2 \\ x----------0.6715 \\ 4x=0.6715 \\ (4x)/(4)=(0.6715)/(4) \\ x=0.17 \\ \\ --- \\ 0.17*12\approx2 \end{gathered}`

Note that we found that approximately 0.17 year is necessary to submerge tat island, converting that to months, we can state that in approximately 2 months