A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the
rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size

a 4.94 sec

b 3.28 sec

c 9.7 sec

d 1.33 sec

Question

A satellite camera takes a rectangular-shaped picture. The smallest region that can be photographed is a 4-km by 4-km rectangle. As the camera zooms out, the length l and width w of the 
rectangle increase at a rate of 3 km/sec. How long does it take for the area A to be at least 4 times its original size

a 4.94 sec

b 3.28 sec

c 9.7 sec

d 1.33 sec

mathstudent55 · Answer

Original area is 4 km x 4 km = 16 m^2
New area is 4 x 16 km^2 = 64 km^2
The new area corresponds to an image that is 8 km by 8 km since 
64 km^2 = 8 km x 8 km
The camerqa has to zoom from 4 km by 4 km to 8 km by 8 km.
Since it zooms at a rate of 3 km/s, to go from 4 km to 8 km, it needs to zoom 4 km at a rate of 3 km/s, so (4 km)/(3 km/s) = 1.33 sec

anonymous · Answer

THANKS @mathstudent55