Math geeks all hands on deck!

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A fellow CCer posed this problem from their kids math book. I came up with an answer that made total sense to me, my father as well. But she says it's wrong. I can't figure out how they came to the 'correct' answer. So i'm posting the question first to see if anyone gets the 'correct' answer AND an explanation of why it's correct. If no one helps i'll post what the math book says is correct, later.

You have one faucet that fills up a pool in 24 hours.
You have second faucet that fills up a pool in 8 hours.
If you run both faucets in one pool, how long does it take to fill up the pool?

I figured out i was approaching the answer wrong. So now i understand where i went wrong. Now i just can't figure out the math to the correct logical approach. So now i understand how to get to the correct answer, I just don't know the math itself.

Will be fun to see everyones answers either way.
 
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Assume that the pool is 48 gallons.

Faucet 1 must be running at 2 gallons per hour. (48 / 24 = 2)

Faucet 2 must be running at 6 gallons per hour. (48 / 8 = 6)

So if you run them both, you have a flow of 8 gallons per hour (2 + 6 = 8), therefore it would take 6 hours to fill up the pool. (8 * 6 = 48)

...Am I right?
 
I grabbed a piece of scratch paper, worked it all out in record time, and came up with...

It's time to buy a bathing suit, if the pool is full.

I think I should stick to my strengths, which don't include math.
 
MissCris said:
I grabbed a piece of scratch paper, worked it all out in record time, and came up with...

It's time to buy a bathing suit, if the pool is full.

I think I should stick to my strengths, which don't include math.
Click to expand...

Yeah...I'm with misscris on this one... POOL PARTY!
 
PopClick said:
Assume that the pool is 48 gallons.

Faucet 1 must be running at 2 gallons per hour. (48 / 24 = 2)

Faucet 2 must be running at 6 gallons per hour. (48 / 8 = 6)

So if you run them both, you have a flow of 8 gallons per hour (2 + 6 = 8), therefore it would take 6 hours to fill up the pool. (8 * 6 = 48)

...Am I right?
Click to expand...

sounds right...
 
Ugly said:
You have one faucet that fills up a pool in 24 hours.
You have second faucet that fills up a pool in 8 hours.
If you run both faucets in one pool, how long does it take to fill up the pool?
Click to expand...

The answer is 6 hours :cool:

If for example, the pool is 24 gallons, then..

faucet #1 pumps 1 gals per hr,
faucet #2 pumps 3 gals per hr..

so both would pump 4 gals per hour. (24gals divided by 4 = 6 hours)
 
This is a "rate of change" problem. The set up is:
Let faucet A = 24 hrs to fill the pool; faucet B = 8 hrs to fill the same pool, and t = time to fill pool in units of hr.

(Rate of faucet A) + (rate of faucet B) = Total rate to fill the pool
( 1 pool / 24 hr ) + ( 1 pool / 8 hr ) = ( 1 pool / t )
( 1/24 ) + (1/8) = 1/t

Now, solve for t.
(1 + 3)/24 = 1/t
4/24 = 1/t
t = 24/4
t = 6 hrs.

Solution: It takes 6 hrs to fill the pool when both faucets are on. :)
 
BananaPie said:
This is a "rate of change" problem. The set up is:
Let faucet A = 24 hrs to fill the pool; faucet B = 8 hrs to fill the same pool, and t = time to fill pool in units of hr.

(Rate of faucet A) + (rate of faucet B) = Total rate to fill the pool
( 1 pool / 24 hr ) + ( 1 pool / 8 hr ) = ( 1 pool / t )
( 1/24 ) + (1/8) = 1/t

Now, solve for t.
(1 + 3)/24 = 1/t
4/24 = 1/t
t = 24/4
t = 6 hrs.

Solution: It takes 6 hrs to fill the pool when both faucets are on. :)
Click to expand...
I like my way better. :p
 
ZeroT,

Your way is peachy indeed, but you don't need to know the size of the pool because that value "cancels" itself out. See?

pool ( 1/24 + 1/8) = pool/t
So, you're really left with the equation: 1/24 + 1/8 = 1/t :p
 
Last edited:
gypsygirl said:
yes, i got approximately 6.2 hours
Click to expand...

i did it slightly different, because it's a lot simpler to do it this way in my head.

oh, and i'm not a cool math geek.

rate of hourly flow of faucet 1: 1/24 = .04
rate of flow hourly flow of faucet 2: faucet 1 x 3 = .12

combined rate of hourly flow =.16

1 / .1 6= ~6.2 hours
 
Last edited:
BananaPie said:
ZeroT,

Your way is peachy indeed, but you don't need to know the size of the pool because that value "cancels" itself out. See?

pool ( 1/24 + 1/8) = pool/t
So, you're really left with the equation: 1/24 + 1/8 = 1/t :p
Click to expand...
You can't really add those unless they has a common de-nom-nom-inator :rolleyes:

So 1/8 = 3/24..

So 1/24 + 3/24 = 4/24

and we all know that 4/24 is just a fancy name for 6 :)
 
gypsygirl said:
i did it slightly different, because it's a lot simpler to do it this way in my head.

oh, and i'm not a cool math geek.

rate of hourly flow of faucet 1: 1/24 = .04
rate of flow hourly flow of faucet 2: faucet 1 x 3 = .12

combined rate of hourly flow =.16

1 / .1 6= ~6.2 hours
Click to expand...

Umm.. Yeah. If you figured this out in your head.... math geek. :p

After reading all this i'm not even going to explain what i went through.
 
i scrolled to the bottom to avoid everyone elses math.

So pump 1 fill the pool in 24 hours or fills 1/24 of the pool per hour
Pump 2 fills the pool in 8 hours or 1/8 of the pool per hour

so with both pumps running in one hour the pool has filled 1/24+1/8. Get common denominators
1/24+3/24=4/24. Simplify to 1/6. So in one hour both pumps filled 1/6 of the pool. Hence it will be filled in 6 hours.
 
I took out my note pad and did the maths problem myself.

I ended up with: "Donuts".

I don't know where on earth you guys get these numbers from.
 
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