Filling a Tub

Date: 6/11/96 at 17:58:49 
From: Michael Balazs
Subject: Word Problem - Filling a Tub

Faucet A will fill a tub in 45 minutes. Faucet B will fill the same 
tub in 20 minutes. How long will it take to fill the tub if both 
faucets are opened at the same time?

For this problem I don't even know where to start. 

Date: 6/11/96 at 18:48:08 
From: Dr. Anthony
Subject: Re: Word Problem - Filling a Tub

Think of the proportion of the tub that is filled PER MINUTE by 
each faucet. 

For A it is 1/45 of the full tub, while for B it is 1/20 of the full tub 
per minute.

So in 1 minute, with A and B together it is 1/45 + 1/20 = 
13/180 of the tub. 

So if t=time, then (13/180)t = 1

t = 180/13 = 13.846 minutes

t = 13 +11/13 minutes

-Doctor Anthony, The Math Forum

Date: Wed, 12 Jun 1996 14:59:23 -0400
From: Michael Balazs
Subject: Re: Word Problem - Filling a Tub

Thank you. What about this one?

A faucet takes 20 minutes to fill an empty tub. The drain takes 50 
minutes to empty the tub when it is full. If both the faucet and the 
drain are opened at the same time, how long will it take to fill the 
empty tub? 

Michael Balazs

Date: Fri, 14 Jun 1996 12:17:40 -0400 (EDT) 
From: Dr. Anthony
Subject: Re: Word Problem - Filling a Tub

You use the same ides as before. The proportion of the tank filled 
per minute by inlet pipe is 1/20, while the proportion emptied per 
minute is 1/50. When operating together the proportion being filled 
is 1/20 - 1/50 = 3/100. 

If t = time to fill the tank under these conditions, then 

t(3/100) = 1

t = 100/3 = 33 +1/3 minutes.

-Doctor Anthony, The Math Forum