Question: Hummingbird Feeder

Comment on Hummingbird Feeder

From where you got 0.75?
greenlight-admin's picture

We're told that the volume decreases by 25%, In other words, it decreases by 1/4
Another way to look at it is to say that 3/4 of the volume remains. So, to find the next volume, we multiply by 3/4

For example, let's start with 8 liters.
One approach is to subtract 1/4 of 8
(1/4)(8) = 2
We get: 8 - 2 = 6

Alternatively, 3/4 of 8 = (3/4)(8) = 6

Same answer either way. HOWEVER, the second one if more convenient/faster

I solved this question using reverse psychology..
as 81/16 = 5.0625 therefore, generating tale

Time : liquid
12 hours from now 5.0625

6 hours from now .75 x A = 5.065 => A= 6.75

Now ( current time) .75 x B = 6.75 => B = 9

6 hours ago .75 x C = 9 => C = 12

therefore answer is 12


A is liquid at time 6 hours from now
B is liquid right now
C is liquid 6 hours ago
greenlight-admin's picture

That works too - well done!

Took a little practice, but now I like table method. You can keep track of what's going on, and it's quick.
greenlight-admin's picture

Good stuff!!

Instead of starting with 6 hours ago as P, why can't you:
1) start with Now = P
2) find P = 81/16=P(.75)^2...then
3) P(1.25) = 6 hours ago?

I wouldn't intuitively think to begin with 6 hours ago being P.
greenlight-admin's picture

Your solution is perfectly valid.
The advantage with letting P = volume 6 hours ago is that, once we solve the equation for P, we have our answer.
That said, your approach works just as well.

Cheers,
Brent

Test the answers will work, too. Luckily, I started with C and that was the correct answer. I drew 4 total boxes. The first 3 boxes were blank and the 4th box was 81/6. So the first box was 12 and I calculated from there (decreasing each by 25%) to arrive at 81/16, and starting with 12 works.

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