🚀 go-pugleaf

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