word problem about time and distince

**lsanger** · April 21st 2010, 12:31 PM

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?

**skeeter** · April 21st 2010, 02:00 PM

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 $y$ = distance traveled south
$x$ = distance traveled east
$z$ = straight-line distance between the two boats

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

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

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

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