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Hello World. I'm Jon Hermiz and am a software engineer here in Michigan. Feel free to look around and leave feedback!

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CS Folks Forgetting Basic Algebra

Its been 10 years since I graduated high school so when this Math problem came up I had to look twice.  My bro was given a little algebra puzzle which I helped him with.  After finishing it up I decided to write it all up and ask fellow co-workers (without giving them answers of course) this same problem.

Whether they could do it or not I didn't really care..I just wanted an answer...any answer.  It is amazing from our IT staff that rarely anyone got it right.  How did folks who got MBAs in MI and BS degrees in various other colleges get stumped by a simple algebra problem. 

I decided to post it here to see what others across the world can come up with.  Its pretty straightforward and a lot of people do have an idea of how to solve it but they always end up saying well there is one piece of missing information..which is true however even with that missing piece you can solve it.

Ok so the problem:

You have a bath tub in which has 4 faucets (I know pretty odd).  One faucet can fill the entire tub in 1 hour.  The second faucet can fill the tub in 45 minutes.  The third faucet can fill it up in 30 minutes.  And finally the last one can fill the entire bath tub in only 15 minutes (note the number of minutes for each faucet is based on the faucet turned on by itself). 

Now that you have this info the problem is how long would it take to fill the tub if all faucets are turned on at the same time?

Here is a photo to help :):

Bathtub (4 faucets)

Please no put downs on wrong answers, this is just for us folks who haven't done some algebra in a real long time!!!  Tell us your answer, draw it if you have to, just give an answer even if you don't know it, post it!

 PS: Mladen you are not allowed to play since you already tried. =)

Print | posted on Sunday, August 19, 2007 11:46 PM | Filed Under [ Other ]

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# re: CS Folks Forgetting Basic Algebra

7 Minutes, 12 seconds.
8/20/2007 1:34 AM | CalmYourself
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# re: CS Folks Forgetting Basic Algebra

28.8 minutes
8/20/2007 1:47 AM | WILDGUESS
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# re: CS Folks Forgetting Basic Algebra

28.8 minutes
8/20/2007 1:47 AM | WILDGUESS
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# re: CS Folks Forgetting Basic Algebra

The taps put in 1, 4/3, 2, 4 tanks per hour respectively. So if they're all on, that should make 8.33 tanks per hour, which means 0.12 hours per tank. 0.12 hours is 7.2 mins, or 7:12
8/20/2007 4:36 AM | Rob
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# re: CS Folks Forgetting Basic Algebra

ha ha... :)
8/20/2007 5:34 AM | Mladen
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# re: CS Folks Forgetting Basic Algebra

7.2 minutes.
8/20/2007 8:39 AM | Siva G
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# re: CS Folks Forgetting Basic Algebra

1/60+1/45+1/30+1/15 = 25/180 = 5/36. 36/5 minutes.
8/20/2007 10:29 AM | Suresh
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# re: CS Folks Forgetting Basic Algebra

Suresh,

We think alike!

Rob,

Didn't think about it in terms of hours, nice job.
8/20/2007 11:50 AM | Jon
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# re: CS Folks Forgetting Basic Algebra

7.2 minutes
8/20/2007 2:47 PM | Matthew
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# re: CS Folks Forgetting Basic Algebra

7.2 minutes.

Suresh's formula is the way to go :)
8/21/2007 12:47 AM | sirrocco
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# re: CS Folks Forgetting Basic Algebra

Common Demoninator is 3 hours, so

3x + 4x + 6x + 12x = 3 hours
25x = 3
x = .12 hours
60 * .04 = 7.2 min = 7min 12 sec

or the verbose method

3 hours = 180 min
60 minute faucet fills 3 tubs in 3 hours
45 minute faucet fills 4 tubs in 3 hours
30 minute faucet fills 6 tubs in 3 hours
15 minute faucet fille 12 tubs in 3 hours

Therefore, in 180 minutes we have filled 25 tubs

25 tubs/180 minutes = 1 tub / x minutes
25x = 180
x = 7.2 minutes
8/21/2007 2:45 AM | David Gugick
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# re: CS Folks Forgetting Basic Algebra

Jon,

My method just seemed to be the most practical, which is generally the easiest way to solve things.

Like the question about "if it takes someone 12 minutes to saw a piece of wood into 3 pieces, how long to cut it into four?", thinking practically is best.

Rob
8/22/2007 6:01 AM | Rob
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# re: CS Folks Forgetting Basic Algebra

To see a concrete example, say the tub is 60 gallons. Then:
Faucet 1 fills 1 gal / minute
Faucet 2 fills 1 1/3 gal / minute
Faucet 3 fills 2 gal / minute
Faucet 4 fills 4 gal / minute
All together, they pour 8 1/3 gal / minute into the tub.
So 60 gallons takes 60 gal / (8 1/3 gal / min) = 7.2 minutes (7 min 12 sec), just as the formulas indicate.

I prefer formulaic solutions, but sometimes a concrete case makes it simple.


Scott
8/22/2007 11:26 AM | Scott
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# re: CS Folks Forgetting Basic Algebra

The problem statement would have been more fun if there also was a drain!

For example, opening the drain empties the bathtub in 4 minutes.

When having an completely open drain, is it still possible to fill the tub with the four faucets?
8/24/2007 7:25 AM | Peter Larsson
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# re: CS Folks Forgetting Basic Algebra

The problem statement would have been more fun if there also was a drain!

For example, opening the drain empties the bathtub in 4 minutes.

When having an completely open drain, is it still possible to fill the tub with the four faucets?
And it it is possible, how long time will it take to fill the tub when drain is open?
8/24/2007 7:26 AM | Peter Larsson
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# re: CS Folks Forgetting Basic Algebra

I got it! Thank goodness you did not ask me to remember calculus...
8/14/2008 9:17 PM | Maitus
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