🚀 go-pugleaf

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
>