Question

The Brazilian free-tailed bat can travel 99 miles per hour. After sunset, a colony of bats emerges from a cave and spreads out in a circular pattern. How long before these bats cover an area of 80,000 square miles? Use π = 3.14

Answer 1

Answer: 1.6 hours.

Explanation:

Ok, the speed of the bats is 99mph.

Here we can think this situation as a circle where the radius is growing at a speed of 99mph.

We assume that the initial radius is r = 0, and we can write the equation of the radius as a linear equation that depends on the time t.

r(t) = 99mi/h*t

First, let's find the radius that we need:

The area of a circle is:

A = ´pi*r^2

If we want A = 80,000 mi^2 we have:

80,000 mi^2 = 3.14*r^2

r = √(80,000 mi^2/3.14) = 159.6 mi

So the radius must be 159.6 miles.

Now, we know that the speed at which the radius increases is 99miles per hour, and we also know that:

Distance = Speed*Time.

in this case:

Distance = 159.6 mi

Speed = 99mi/h

Time = is the thing we want to find.

159.6mi = 99mi/h*T

T = 159.6mi/99mi/h = 1.6 hours.