Help - someone gave this puzzle to my 9 year old for a bit of fun to see if he can work it out - I've tried several times but don't seem to get anywhere................
A bath takes 5 minutes to fill with the plug in. It takes 8 minutes to empty when you take the plug out. How long does it take for the bath to fill with the plug out ?
Cheers
Andrew
2006-09-04 19:46:02 · 61 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
In one minute, 20% (1/5) of the tub can be filled, plug in.
With the drain out, the tub loses 12.5% (1/8) of the water in a minute.
Filling it with the drain out:
adding 20%
draining 12.5%
For a net gain 7.5% every minute
It will take 13 1/3 minutes to fill the tub.
2006-09-04 19:52:53 · answer #1 · answered by Jim S 5 · 3⤊ 1⤋
If the bath takes 5 minutes to fill with the plug in and it takes 8 minutes for the bath to empty then the proportion inflow to outflow is for every minute you fill it will out will lose only 5/8 of the water. Therefore to fill the bath up to the capacity of 1 minute of water would take 2 minutes 40 seconds (1/ 0.375 where 0.375 is 3/8ths). To fill the bath up completely would therefore take 13 minutes and 20 seconds (5*160 seconds). This is not taking into account any graviational force or any extra downward pressure caused by the water as the bath fills.
2006-09-05 02:01:13 · answer #2 · answered by Careen K 1 · 1⤊ 0⤋
let V be the volume of the bath
Q be the flowrate to fill with the plug in
Q1 be the flowrate to empty
Q2 be the flowrate to fill with the plug out
t2 be the time to fill the bath when plug out
volume is flowrate times time and this works in SI unit. Therefore we should take SI (standard interrnational) unit of time which is second.
V = 5x60xQ = 8x60xQ1
from the above equation we get Q = 8/5Q1
to fill the bath when the plug is out the flowrate will be Q - Q1
i.e. Q2 =8/5Q1 - Q1
since the volume of the bath is constant
V = 8x60xQ1 = Q1(8/5 - 1) t2
eliminating Q1 from the above equation we get
8x60 = (8/5 - 1)t2 = 3/5t2
this emplies t2 = (8x60)(5/3) = 800 seconds
Therefore the time to fill the bath when plug out will be 800seconds or 13.333... minutes
2006-09-04 22:11:19 · answer #3 · answered by mas 2 · 1⤊ 0⤋
I have no answer. I just wanted to comment on how many people really aren't reading the question! So many people say, "The plug is out! The plug is out! It will never fill!" that they don't take time to notice that the drain rate is slower than the fill rate. Yes, water is always flowing out, but the water level will still rise because it's coming in faster. If the water level is rising, then it will eventually reach the top. By definition, the tub will then be FULL! So yes, it can fill up.
I think my favorite useless answer is from the person who said they tried it in their OWN bathtub and it never got more than a thin layer of water; therefore, the tub in YOUR question must never be able to fill up, either! #-o
2006-09-09 07:24:50 · answer #4 · answered by cjxctx 2 · 0⤊ 0⤋
A bath doesn't fill up if the plug is out because, when the water gets to a certain level in the bath the pressure of the water will force the water out of the bath quicker.
2006-09-09 07:19:05 · answer #5 · answered by Anonymous · 0⤊ 0⤋
13 min. 20 sec.
The tub fills up in 5/8 of the time it takes to drain it. As long as the water is running in faster than it drains out, it will eventually fill up. That 's common sense. The faucet is adding water 1.6 times as fast as water is running out the drain. That means that in the time that it would take to add 8 gallons, for example, 5 gallons will run out if the drain is open, so only 3 gallons have been added in that same amount of time. With the drain open, the water is filling at a rate of 3/8 as fast as it would if the drain were closed. It would take 8/3 as long to fill the tub this way.
8/3 x 5 min. = 13 min. 20 sec.
2006-09-09 15:45:58 · answer #6 · answered by ? 4 · 1⤊ 0⤋
With the drain out, the tub loses 12.5% (1/8) of the water in a minute.
Filling it with the drain out:
adding 20%
draining 12.5%
For a net gain 7.5% every minute
It will take 13 1/3 minutes to fill the tub.
2006-09-10 04:24:44 · answer #7 · answered by green_maths_scout 2 · 1⤊ 0⤋
I've just calculated how deep my bath must be to empty in 5 mins and how fast i must have the tap on to fill back to the same level in 8 ... when i tried to fill it without the plug in ... someone came to the front door ... so i'm not sure
2006-09-05 06:23:56 · answer #8 · answered by Gary H 2 · 0⤊ 1⤋
Tough problem for a 9 yr old.
I like to think of it as... you want to fill the tub 1 more time than you're draining the tub. So for example in 10 minutes you'd be filling the tub 2 times (10/5), but draining it 1.25 times (10/8)
so the equation to set up is something like:
x/5 - x/8 = 1 , where x is the time
# of times to fill the tub in 5 min - # of times to drain the tub = 1 (full tub)
the answer works out to 13.333 min where you fill the tub 2.66 times and drain it 1.66 for a full tub
2006-09-04 19:57:00 · answer #9 · answered by Scott S 2 · 2⤊ 0⤋
I am not sure what the answer is either Andrew - but to all those people who say it won't fill, try reading the question. It takes less time to fill by 3 minutes than to empty. If you fill the bath for 5 minutes, then empty it for 5 minutes, there will still be water in..................so the inflow is greater than the outflow.
2006-09-05 00:44:05 · answer #10 · answered by blueeyedboy3004 2 · 1⤊ 1⤋