Question

Tom and Jerry are jogging in the woods along straight, level paths that
intersect at right angles. Tom is 3 miles from the intersection and jogging away from it at
the rate of 2 miles per hour. Jerry is 4 miles from the intersection and is jogging away
from it at the rate of 3 miles per hour. At what rate is the distance between Tom and Jerry
increasing?

Answer 1

3.6 miles per hour. Care for an explanation? hehe!

Answer 2

yeah please

Answer 3

\(z^2 = x^2 + y^2\)

\( 2z\dfrac{dz}{dt} = 2x\dfrac{dx}{dt} + 2y\dfrac{dy}{dt} \)

\( z\dfrac{dz}{dt} = x\dfrac{dx}{dt} + y\dfrac{dy}{dt} \)

\( \dfrac{dz}{dt} = \dfrac{ x \dfrac{dx}{dt} + y \dfrac{dy}{dt}}{z} ~~~~~(1)\)

Plug in the values below into equation (1) above to find the answer.

\( x = 3, ~\dfrac{dx}{dt} = 2, ~y = 4, ~\dfrac{dy}{dt} = 3\)

\(z = \sqrt{3^2 + 4^2} = 5\)

Answer 4

Thank you that was a awesome respond

Answer 5

You're welcome.