Help. Help. Help.
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?

Question

Help. Help. Help.
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?

anonymous · Answer

A) 4.94 sec
B) 3.28 sec
C) 9.7 sec
D) 1.33 sec

anonymous · Answer

what is the region of the photograph when the area is 4 times the original size? maybe we can start here

anonymous · Answer

Alright! so..

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

aww, i was going to work with him to get to this point! careful about giving the answer right away unless they ask for it

anonymous · Answer

Oh my gawsh. I suck at word problems. @jeremyggg You can still do that! I like to understand, not just get an answer. But thank you so much @Light&Happiness !!! Oh, and I'm a female. ;P

anonymous · Answer

Glad i could help.

anonymous · Answer

ooh i'm sorry! well, the first step was figuring out the new area! you learned that the area of a rectangle is l x w i am sure. i could walk you through it but the breakdown that @Light&Happiness is pretty good and seems to be a proper way to go (wouldn't the new dimensions be 8x8 though and not 4x16?)

anonymous · Answer

I have no idea. I'm in 11th grade, and 4 honors classes, and can't seem to get the easy problems.. v_v

anonymous · Answer

Hey, I think I just did it. :D

anonymous · Answer

Thanks guys! @jeremyggg @Light&Happiness ! God bless you both! :DDD

anonymous · Answer

Why the poop does your name not show up? Sheesh..

anonymous · Answer

hahah! it didn't show up when i did it either.

anonymous · Answer

Hahaha, No problem. God bless you as well..!

anonymous · Answer

Everyone give someone else a medal since I can't give you both one. Lol.

anonymous · Answer

Yay. :3