Question

A bear was seen near a campground. Searchers were dispatched to the region to find the bear.

A. Assume the bear can walk in any direction at a rate of 2 miles per hour. Suppose the bear was last seen 4 hours ago. How large an area must the searchers cover? Use 3.14 for pi. ROund your answer to the nearest square mile. ___________
B. How much additional area would the searchers have to cover if the bear were last seen 5 years ago?

Answer 1

Explanation:

Given data:

Rate of walk of bear is 2 miles per hour

Bear was seen 4 hr before

The bear can walk 8 miles (2× 4) since it is walking 2 miles/hr for 4 hr, therefore radius of then 8

Use areas of circle to calculate the area cover by searcher

`A = \pi r^2`

`A = \pi (8)^2 = 201`

b) when bear seen 5 hr ago thus

The bear can walk 8 miles (2× 5) since it is walking 2 miles/hr for 4 hr, therefore radius of then 10

Use areas of circle to calculate the area cover by searcher

`A = \pi r^2`

`A = \pi (10)^2 = 314`

Additional area = 314 - 201 = 113

Answer 2

A. The searchers should cover the greatest area which can be calculated by assuming that the distance covered by the bear for 4 hours is the radius of the circle.
radius = (2 miles/hour)(4 hours) = 8 miles
area = 2(3.14)(8 miles)² = 401.92 mi²

B. I would assume that for this number, we are to solve the additional area to be covered if the bear was last seen 5 HOURS ago.
radius = (2 miles/hour)(5 hours) = 10 miles
area = (2)(3.14)(10 miles)² = 628 mi²

We get the answer for B by subtracting the two areas which will give us an answer of 226.08 mi².