🚀 go-pugleaf

rate   time    
cold   1/9    t       
warm   1/12   t       

t/9 + t/12 = 1

LCD = 36

4t + 3t = 36

7t = 36

t = 36/7

t = 5 and 1/7 minutes

In article <6tgc6c$rqg$1@readme.online.no>, Marie M. Moltubakk
<mamoltub@online.no> writes
>I'm not sure this is the right place to ask, but I will try anyways. I
>attend an upper secondary school, and my teacher has just given us this:
>
>Someone has a bath tub, and it is to be filled with water. If you tap cold
>water, it takes 9 minutes to fill it. If you tap warm water, it takes 12
>minutes. How much time will it take if you use both warm and cold water?
>
>In my opinion there are more than one solution to this, because it depends
>on the bath tub. (Are there one or two taps, does the water run in the same
>speed or twice as fast when both warm and cold water is on?)
>
>I have found one solution yet (two taps, double speed):
>
>I set the size of the bath tub to 300 liters.
>Cold water: 33,33 liters/minute
>Warm water: 25 liters/minute
>
>33,33x+25x=300
>x=5,14
>
>So, it would take 5 minutes and 8 seconds to fill the bath tub. Is this
>right, and what are the other ways to do it? This is probably easy for you
>skilled people, but not for me... Thanks in advance!
>
>--
>~Mmm
>*http://privat.riksnett.no/~arve.moltubakk/mmm/*
>
>
The method is fine but why choose a particular value for the volume?
If your answer depends on this value then it is obviously wrong.

So if volume of bath = V,
Cold water rate = V/9
Hot  water rate = V/12

Therefore rate of both together =
V/9 + V/12 = (4 X V + 3 X V)/36 = 7 X V/36

Hence time to fill the bath = V / (7 X V/36)
= 36 / 7 minutes = 5 minutes & 60/7 seconds
i.e. about 5 minutes and 9 seconds

-- 
Jeremy Boden

Marie M. Moltubakk wrote:
> 
> I'm not sure this is the right place to ask, but I will try anyways. I
> attend an upper secondary school, and my teacher has just given us this:
> 
> Someone has a bath tub, and it is to be filled with water. If you tap cold
> water, it takes 9 minutes to fill it. If you tap warm water, it takes 12
> minutes. How much time will it take if you use both warm and cold water?
> 
> In my opinion there are more than one solution to this, because it depends
> on the bath tub. (Are there one or two taps, does the water run in the same
> speed or twice as fast when both warm and cold water is on?)
> 
> I have found one solution yet (two taps, double speed):
> 
> I set the size of the bath tub to 300 liters.
> Cold water: 33,33 liters/minute
> Warm water: 25 liters/minute
> 
> 33,33x+25x=300
> x=5,14
> 
> So, it would take 5 minutes and 8 seconds to fill the bath tub. Is this
> right, and what are the other ways to do it? This is probably easy for you
> skilled people, but not for me... Thanks in advance!
> 
> --
> ~Mmm
> *http://privat.riksnett.no/~arve.moltubakk/mmm/*

This is a clone of the "two guys are painting a room..." problem.
The "fast" trick is to take the product of the rates /sum of the rates.

I had a Student in College  Intermediate Algebra ( for about five days)
who had got the impression that EVERY problem involving two different 
numbers could be worked this way.
Ah..New MAth!!!

Marie M. Moltubakk (mamoltub@online.no) wrote:
: I'm not sure this is the right place to ask, but I will try anyways. I
: attend an upper secondary school, and my teacher has just given us this:

: Someone has a bath tub, and it is to be filled with water. If you tap cold
: water, it takes 9 minutes to fill it. If you tap warm water, it takes 12
: minutes. How much time will it take if you use both warm and cold water?

: In my opinion there are more than one solution to this, because it depends
: on the bath tub. (Are there one or two taps, does the water run in the same
: speed or twice as fast when both warm and cold water is on?)

: I have found one solution yet (two taps, double speed):

: I set the size of the bath tub to 300 liters.
: Cold water: 33,33 liters/minute
: Warm water: 25 liters/minute

: 33,33x+25x=300
: x=5,14

: So, it would take 5 minutes and 8 seconds to fill the bath tub. Is this
: right, and what are the other ways to do it? This is probably easy for you
: skilled people, but not for me... Thanks in advance!

The standard assumption in problems of this sort is that the flow rate
for both hot and cold is the sum of the flow rates for hot and cold taken
separately.  If you are supposed to make some other assumption, the
problem should state that.  (Unless you are studying fluid mechanics,
in which case you should have studied the previous chapters and be
able to choose the right assumption yourself.)

For extra credit:

1.  Show that the answer doesn't depend on how large the bathtub is.

2.  Work out the answers for some of the alternate assumptions you give,
and ask your teacher whether or not you got them right.

3.  Suppose that there is a leak in the bathtub, so that a full bathtub
will drain to empty in 30 minutes.  How long does it take to fill with
both hot and cold water?  

Paul Hughett

Robert J. Pease wrote:

> This is a clone of the "two guys are painting a room..." problem.
> The "fast" trick is to take the product of the rates /sum of the rates.
>
> I had a Student in College  Intermediate Algebra ( for about five days)
> who had got the impression that EVERY problem involving two different
> numbers could be worked this way.
> Ah..New MAth!!!

Oh great, I hate this new math.  It started in my high school when I was a sophomore.
After 3 years in it, they couldn't do standard Geometry, let alone Trig.  After 3 years
you had the option of going to AP Calculus...I don't know a single person who wanted to.
Sure, I took AP Calculus, and passed the BC test with a 4, but I didn't take this "new
math" crap.


Dwayne

In article <6tgc6c$rqg$1@readme.online.no>, "Marie M. Moltubakk"
<mamoltub@online.no> wrote:

> I'm not sure this is the right place to ask, but I will try anyways. I
> attend an upper secondary school, and my teacher has just given us this:
> 
> Someone has a bath tub, and it is to be filled with water. If you tap cold
> water, it takes 9 minutes to fill it. If you tap warm water, it takes 12
> minutes. How much time will it take if you use both warm and cold water?
> 
> In my opinion there are more than one solution to this, because it depends
> on the bath tub. (Are there one or two taps, does the water run in the same
> speed or twice as fast when both warm and cold water is on?)
> 

If you assume that turning one tap on or off does not affect the rate of
flow from the other tap, as is usual in these problems, then

the cold tap alone fills 1/9 of tub per minute, 
the hot tap alone fills 1/12 of the tub per minute,
together thy fill 1/9 + 1/12 = 7/36 of the tub per minute.

Thus it takes 36/7 minutes = 5 1/7 minutes to fill the tub.

Several people have responded to Marie's post and no one has pointed out the
contradiction between her assumption and her solution.

The original poster asked, "does the water run in the same speed or twice as
fast when both warm and cold water is on?" Since the speeds for the warm
water and the cold water are clearly different, this question makes no sense
(although what the poster is trying to say is pretty evident).

Marie specifically states that she is assuming "double speed", but then uses
a speed which is the SUM of the individual speeds and NOT "double" the speed
of ANYTHING.

The underlying question, of course, is whether the flow rate from one tap is
independent of the flow rate from the other tap (as Paul points out). Unless
the context of the course implies otherwise (such as a fluid dynamics
course) this is the only reasonable assumption to make.

Paul Hughett wrote in message <6th2q0$hui$1@netnews.upenn.edu>...
>Marie M. Moltubakk (mamoltub@online.no) wrote:
>: I'm not sure this is the right place to ask, but I will try anyways. I
>: attend an upper secondary school, and my teacher has just given us this:
>
>: Someone has a bath tub, and it is to be filled with water. If you tap
cold
>: water, it takes 9 minutes to fill it. If you tap warm water, it takes 12
>: minutes. How much time will it take if you use both warm and cold water?
>
>: In my opinion there are more than one solution to this, because it
depends
>: on the bath tub. (Are there one or two taps, does the water run in the
same
>: speed or twice as fast when both warm and cold water is on?)
>
>: I have found one solution yet (two taps, double speed):
>
>: I set the size of the bath tub to 300 liters.
>: Cold water: 33,33 liters/minute
>: Warm water: 25 liters/minute
>
>: 33,33x+25x=300
>: x=5,14
>
>: So, it would take 5 minutes and 8 seconds to fill the bath tub. Is this
>: right, and what are the other ways to do it? This is probably easy for
you
>: skilled people, but not for me... Thanks in advance!
>
>The standard assumption in problems of this sort is that the flow rate
>for both hot and cold is the sum of the flow rates for hot and cold taken
>separately.  If you are supposed to make some other assumption, the
>problem should state that.  (Unless you are studying fluid mechanics,
>in which case you should have studied the previous chapters and be
>able to choose the right assumption yourself.)
>
>For extra credit:
>
>1.  Show that the answer doesn't depend on how large the bathtub is.
>
>2.  Work out the answers for some of the alternate assumptions you give,
>and ask your teacher whether or not you got them right.
>
>3.  Suppose that there is a leak in the bathtub, so that a full bathtub
>will drain to empty in 30 minutes.  How long does it take to fill with
>both hot and cold water?
>
>Paul Hughett
>

On Sun, 13 Sep 1998 13:59:50 +0200, "Marie M. Moltubakk"
<mamoltub@online.no> wrote:

>I'm not sure this is the right place to ask, but I will try anyways. I
>attend an upper secondary school, and my teacher has just given us this:

>Someone has a bath tub, and it is to be filled with water. If you tap cold
>water, it takes 9 minutes to fill it. If you tap warm water, it takes 12
>minutes. How much time will it take if you use both warm and cold water?

>In my opinion there are more than one solution to this, because it depends
>on the bath tub. (Are there one or two taps, does the water run in the same
>speed or twice as fast when both warm and cold water is on?)

The intended interpretation is almost certainly the one you used: that
the rates of flow of hot and cold water are fixed and independent of
which taps are on.

>I have found one solution yet (two taps, double speed):

>I set the size of the bath tub to 300 liters.

How do you know that you wouldn't get a different answer if you made a
different assumption about the size of the tub?  In fact your method
will give you the right answer no matter what size you assume, but
could you demonstrate this?  (Let V be the volume of the tub in
litres.  Then the cold water flows at V/9 litres/min. and the hot at
V/12 l./min.  If it takes x min. to fill the tub when both are
running, (V/9)x + (V/12)x = V.  Divide by V and solve for x.)

>Cold water: 33,33 liters/minute

It would be better to use the exact value of 33 1/3.

>Warm water: 25 liters/minute

>33,33x+25x=300
>x=5,14

100x/3 + 25x = 300; 175x = 900; x = 900/175 = 36/7 = 5 1/7 min., which
is actually 5 min. 9 sec. when rounded to the nearest second.  (Here's
where you paid for not using the exact rate of flow of the cold
water.)

>So, it would take 5 minutes and 8 seconds to fill the bath tub. Is this
>right, and what are the other ways to do it? This is probably easy for you
>skilled people, but not for me... Thanks in advance!

I already sketched a general version of your approach.  Here's another
way to think about such problems.  The cold water alone fills 1/9 of
the tub in one minute.  The hot water alone fills 1/12 of the tub in
one minute.  If both are flowing, they will fill 1/9 + 1/12 = 7/36 of
the tub in one minute.  Therefore they will need 36/7 min. to fill the
tub.

Brian M. Scott
(posted and mailed)

William L. Bahn wrote:

> Several people have responded to Marie's post and no one has pointed out the
> contradiction between her assumption and her solution.

It seemed likely to have been a minor language problem.

Brian M. Scott

In 12 minutes running the warm tap only would produce 1 tub of water.
In 12 minutes running the cold tap only would produce 4/3 tub of water.
 12 minutes of running warm and cold would produce 7/3 tubs of water

So 1 tub of warm and cold would take 12/(7/3) = 5.14 minutes 
Approx 5 minutes and 8.6 seconds

Marie M. Moltubakk <mamoltub@online.no> wrote in article
<6tgc6c$rqg$1@readme.online.no>...
> Someone has a bath tub, and it is to be filled with water. If you tap
cold
> water, it takes 9 minutes to fill it. If you tap warm water, it takes 12
> minutes. How much time will it take if you use both warm and cold water?

>Someone has a bath tub, and it is to be filled with water. If you tap cold
>water, it takes 9 minutes to fill it. If you tap warm water, it takes 12
>minutes. How much time will it take if you use both warm and cold water?

...

Thanks for your help, everyone! I have worked out a few examples now, and I
learnt a lot from this. Sorry about the language problems... English is not
my mother tounge.

--
~Mmm
*http://privat.riksnett.no/~arve.moltubakk/mmm/*

Marie M. Moltubakk wrote:

[snip]

> l Sorry about the language problems... English is not
> my mother tounge.

No need to apologize: you write it very well.

Brian M. Scott