a bug crawls clockwise around the outside rim of a clock from 12 to 4 and travels 7 inches. if a second bug crawls around the outside rim from 6 to 11, in the same direction, how many inches did the bug crawl?

I'll be glad to check your answer.

To calculate the distance the second bug crawled, we need to find the circumference of the clock.

The circumference of a circle is given by the formula:
Circumference = 2 * π * radius

In this case, the clock represents a circle. The radius is the distance from the center of the clock to any point on the edge.

Given that the first bug crawls from 12 to 4 and travels 7 inches, we can calculate the circumference of the clock.

To calculate the radius, we can divide the total distance traveled by the first bug by the fraction of the clock's circumference it covered. The fraction can be found by dividing the angle (in degrees) covered by the bug (from 12 to 4) by a complete circle (360 degrees).

Angle Covered by First Bug = 4 - 12 = -8 hours (assuming we are using a 12-hour format)
360 degrees = 12 hours

Fraction Covered by First Bug = -8 hours / 12 hours

Now, we can calculate the circumference of the clock using the equation:

Circumference = 2 * π * radius

Circumference = 2 * π * (Distance Traveled by First Bug / Fraction Covered by First Bug)

Circumference = 2 * π * (7 inches / ( -8 hours / 12 hours))

Once we have the circumference, we can calculate the distance traveled by the second bug. This can be done by dividing the angle covered by the second bug (from 6 to 11) by a complete circle (360 degrees) and multiplying it by the circumference.

Angle Covered by Second Bug = 11 - 6 = 5 hours
Fraction Covered by Second Bug = 5 hours / 12 hours

Distance Traveled by Second Bug = Fraction Covered by Second Bug * Circumference

By substituting the values into the formula, we can find the distance traveled by the second bug.