Expert: Paul Klarreich - 12/29/2009

Question
Two roads cross at right angles, one running north/south and the other east/west. Eighty feet south of the intersection is an old radio tower. A car traveling at 50 ft per sec passes through the intersection heading east. At how many feet per sec is the car moving away from the radio tower 3 secs after it passes through the intersection?
a) 43.65 B) 44.12 C) 44.59 D) 56.67 E) 81.76

I have tried numerous of ways including finding dy/dt and dx/dt but have not come to answer anywhere close to any of the choices. Please help. Thank you

Answer
Questioner: Nicky
Country: United States
Category: Calculus
Private: No
Subject: Word problem
Question: Two roads cross at right angles, one running north/south and the other east/west. Eighty feet south of the intersection is an old radio tower. A car traveling at 50 ft per sec passes through the intersection heading east. At how many feet per sec is the car moving away from the radio tower 3 secs after it passes through the intersection?
a) 43.65 B) 44.12 C) 44.59 D) 56.67 E) 81.76

I have tried numerous of ways including finding dy/dt and dx/dt but have not come to answer anywhere close to any of the choices. Please help. Thank you
...................................
This is a related rates problem. (Look them up on the site -- there are lots of them.)

Variables:

x = distance from crossing.
z = distance from tower.

Rates:

dx/dt = 50
dz/dt to be found.

Relation:

x^2 + 80^2 = z^2

You can handle the rest.