🚀 go-pugleaf

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)