# Question: Hummingbird Feeder

## Comment on Hummingbird Feeder

### hi brent

hi brent
is there any other way to solve this question ? ### Sorry, but I can't think of

Sorry, but I can't think of an alternate solution offhand.

the volume decreases 1/4 every 6 hours, so the volume every 6 hours is 3/4 of the current volume.
to go back in time, I multiply by the inverse of 3/4 which is 4/3

P+12 = 81/16
P+6 = (81/16) * 4/3 = 27/4
P = (27/4) * 4/3 = 9
P-6 = (9) * 4/3 = 12 ### That definitely works - nice

That definitely works - nice job!!

Brilliant!

### Hi Brent,

Hi Brent,
Instead of 6 hrs ago i started my calculation from 'now' which i got as 9 (if I compare from your table it's correct)..but then how will i proceed further to calculate for 6 hrs ago. ### If we start at NOW, we get:

If we start at NOW, we get:

Let V = Volume NOW.

NOW: V
6 hrs from now: (3/4)V
12 hrs from now: (3/4)(3/4)V

So we get: (3/4)(3/4)V = = 81/16
Simplify: (9/16)V = 81/16
Multiply both sides by 16 to get: 9V = 81
Solve: 9
So, the present volume is 9 ounces

To find the volume 6 hours in the FUTURE, we take the present volume and MULTIPLY by 3/4.

To find the volume 6 hours in the PAST, we take the present volume and DIVIDE by 3/4.

So, volume 6 hours ago = 9 ÷ 3/4
9 ÷ 3/4 = 9 x 4/3 = 12

Cheers,
Brent

### To avoid big numbers I

To avoid big numbers I converted 81/16 to 3^4/4^2 and so(3/4)^3*P = (3/4)^3 * (3/4^-1) then P=3/1/4 so P=3*4 =12 Very nice!!

### you know what I do? I did it

you know what I do? I did it this way,

(3/4)x*(3/4) = 81/16, x = 9, 0.75x = 9, x = 12 ### I'm not sure what those steps

I'm not sure what those steps mean. Do you care to elaborate?

### so 3/4 is 75%, decrease 1/4

so 3/4 is 75%, decrease 1/4 (25% every 6 hours), so let the current equal to x, x(1-0.25)(1-0.25)[decreased by 25% for two times), so current solved to be 9 ounces, then the target question asks for 6 hours ago which means (x-0.25) = 9, so x = 12 Perfect!