Question

The Brazilian three-tailed bat can travel 99 mph. 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 mi.²?

a) 808.08 hours
b) 4.04 hours
c) 808.08 minutes
d) 0.04 hours

Answer 1

To find the time for bats to cover 80,000 square miles, calculate the radius of the circle using the formula for a circle's area, then divide the radius by the bat's speed of 99 mph to determine the time.

Step-by-step explanation:

To calculate the time it will take for Brazilian three-tailed bats to cover an area of 80,000 square miles, we need to determine the radius of the area that corresponds with this surface area when spread in a circular pattern. This requires knowledge of the formula for the area of a circle, which is Area = πr^2 where π is the constant Pi (approximately 3.14159) and r is the radius of the circle.

First, solve for r by manipulating the formula to r = √(Area/π). Substituting 80,000 square miles for the area gives us the radius. The bats travel at 99 mph, and to find the time taken to travel this distance we use the formula Time = Distance/Speed, substituting the previously found radius for distance and 99 mph for speed.