SOLUTION: if it takes the faucet 21 minutes to fill the tub, and it takes the drain 28 minutes to empty the tub, how long will it take to fill the tub, if grandma forgets to close the drain

Click here to see ALL problems on Human-and-algebraic-language

Question 63914: if it takes the faucet 21 minutes to fill the tub, and it takes the drain 28 minutes to empty the tub, how long will it take to fill the tub, if grandma forgets to close the drain while filling it?
Found 2 solutions by rajagopalan, tanimachatterjee:
Answer by rajagopalan(174) (Show Source):
You can put this solution on YOUR website!
You solve it like this:
Filling time 21 min
Filling Rate 1/21 of the tub per minute....A
Draining Rate 1/28 of the tub per minute....B
So, Net Filling rate (NFR) = A-B = (1/21) - (1/28)
Taking LCM of 84, we get NFR = (4/84)-(3/84)=1/84
For filling 1/84 of the tub it takes 1 minute
for filling full tub ie 84/84 it will take 84 minutes.
Good day..
Cross Check :
In 84 minutes the fill pipe will pour 4 times the tub volume
In 84 minutes the Drain pipe will drain 3 times the tub volume
We have one volume of water in tub.
Ok!

Answer by tanimachatterjee(60) (Show Source):
You can put this solution on YOUR website!
in 1 min faucet fills 1/21 part of the tub.
and in 1 min 1/28 part goes out
so in 1 min (1/21 - 1/28)part of the tub is filled
= 1/84 part
faucet takes 84 min to fill the tub