# Thread: word problem about time and distince

1. ## word problem about time and distince

mike and john are in boats located at the center of a lake. At time t=0, Sonya begins travelling south at a speed of 36 mph. At the same time, Isaac takes off, heading east at a speed of 27 mph. How fast is the distance between them changing after 12 minutes?

2. Originally Posted by lsanger
Sonya and Isaac are in motorboats located at the center of a lake. At time t=0, Sonya begins travelling south at a speed of 36 mph. At the same time, Isaac takes off, heading east at a speed of 27 mph. How fast is the distance between them changing after 12 minutes?
let $\displaystyle y$ = distance traveled south
$\displaystyle x$ = distance traveled east
$\displaystyle z$ = straight-line distance between the two boats

given $\displaystyle \frac{dx}{dt}$ and $\displaystyle \frac{dy}{dt}$ ... question asks for $\displaystyle \frac{dz}{dt}$ after 12 minutes = (0.2 hr)

$\displaystyle z^2 = x^2 + y^2$

take the time derivative, calculate $\displaystyle x$, $\displaystyle y$, and $\displaystyle z$ for t = 12 minutes and solve for $\displaystyle \frac{dz}{dt}$