Question

Ap calc

Two boys begin running from point C. One moves north while the other moves west. When the first boy is four miles north, he is running at 12 miles per hour. Simultaneously, the second boy is 2.5 miles west of C and is running at
8 miles per hour. Find the rate at which the two boys are separating at that instant.

Answer 1

Answer: The rate at which the two boys are separating is 14.4 mph.

Explanation: The rate at which the two boys are separating can be found using the Pythagorean theorem.

Let's call the rate at which they are separating "R".

Using the Pythagorean theorem, we have:

R^2 = (12)^2 + (8)^2

Taking the square root of both sides:

R = √(12^2 + 8^2) = √(144 + 64) = √208 = 14.4 mph

So the rate at which the two boys are separating is 14.4 mph.