Here is the text of my problem:

*A boy is flying a kite at a height of 150ft. If the kite moves gorizontally away from the boy at 20ft/s, how fast is the string being paid out when the kite is 250ft from him?* **Given:** - y=150ft
- x=250ft
- $\displaystyle \frac{dx}{dt} = 20ft/s$

**Find:** - $\displaystyle \frac{dz}{dt} when x = 250$

**Work:** - by the theorem of pythagoras:

- $\displaystyle z = 50\sqrt{34}$

- $\displaystyle \displaystyle\frac{dz}{dt} = \frac{x*\frac{dx}{dt} + y*\frac{dy}{dt}}{z}$

- $\displaystyle \displaystyle\frac{dz}{dt} = \frac{(250*20)+ (150*0)}{50\sqrt{34}}$

- $\displaystyle \displaystyle\frac{dz}{dt}=\frac{5000}{50\sqrt{34} }= \frac{100}{\sqrt{34}}}$

The book goves an answer of

**16ft/s**. Can someone give me a hint of where I might have gone astray? Thanks!