Brain Teaser

[54warrior]

This was sent to me in an email, I think I have the answer.

You can fill the tub from the cold water tap in 6 minutes and 40 seconds, while it takes

exactly 8 minutes to fill it from the hot water tap. After the tub if full, and you pull out the

stopper, it takes the water exactly 13 minutes and 20 seconds to run out. ~

Now, if you leave the stopper out and open both the hot and cold water taps all the way,

how long will it take to fill the tub???????

[Skyboi]

Uhhhhhh......... FOREVER?

[54warrior]

Nope, the cold and hot water are filling the tub at a faster speed than the drain is draining it, there is an answer

[Quartz]

300 seconds (5 minutes).

[kman]

i know nothing about the dynamics of hydraulics but a wild azz guess says assuming the flow rate of hot and cold water will offset each other equally when both are turned on, i say it will take approximately 13 minutes 20 seconds to fill it. (13.33/(6.66 + 8)/2) * (6.66 + 8)/2 = 13.33 or 13 minutes 20 seconds.

[PuvMan]

Originally Posted by Quartz

300 seconds (5 minutes).

thats what i got

(Rh + Rc - Ro) * t = 1

8Rh = 1
6.66Rc = 1
13.2Ro = 1

Rh = .125
Rc = .15
Ro = .075

(.125 + .15 - .075) * time = 1
1 / .2 = 5

-----------------------------
edit: although, a full tub will drain at a faster rate to begin with than a 1/2 full tub due to increased pressure (both with diminishing returns)............. so then we would need to use some crafty calculus to determine the true answer.

[Quartz]

Originally Posted by PuvMan

edit: although, a full tub will drain at a faster rate to begin with than a 1/2 full tub due to increased pressure (both with diminishing returns)............. so then we would need to use some crafty calculus to determine the true answer.

Yea but who wants to do differential calculus for a brain teaser. Not me.

[baseballfanz]

What a waste of water.

[Juday]

13 minutes 20 sec....give or take a few....

[PuvMan]

The World's Biggest Puzzle Book - Google Book Search

[kman]

oh yeah i see how my calc is way wrong. You guys (quartz and puvman) are you assuming there is both a hot and cold water spout flowing into the tub separately, otherwise if it was a typical setup flowing into one spout would that not cause a capacity contraint when both hot and cold are turned on? What would your answer be if one spout? 7.69 minutes?

[Juday]

So what's the freakin' answer already? I know I got it wrong, but I'm curious for the answer and how it's solved.

[Quartz]

Originally Posted by Juday

So what's the freakin' answer already? I know I got it wrong, but I'm curious for the answer and how it's solved.

The answer is 5 minutes.

There are many ways of figuring this out but here's how I did it. To make the math easier I assumed a tub that holds 100 gallons

Divide 100 by the time (in seconds) that it takes to fill with cold water. Repeat this for the hot water. Add these two numbers together and you will get the rate at which the tub will fill up in gals per second.

Now divide 100 by the time it takes to empty the tub. This will give you the rate that the tub empties at in gals per second.

Subtract the rate the tub empties from the rate the tub fills and you get your actual fill rate.

Now divide 100 by the actual fill rate and you get the answer in seconds.

I hope this helps.

[kman]

Originally Posted by Quartz

The answer is 5 minutes.

There are many ways of figuring this out but here's how I did it. To make the math easier I assumed a tub that holds 100 gallons

Divide 100 by the time (in seconds) that it takes to fill with cold water. Repeat this for the hot water. Add these two numbers together and you will get the rate at which the tub will fill up in gals per second.

Now divide 100 by the time it takes to empty the tub. This will give you the rate that the tub empties at in gals per second.

Subtract the rate the tub empties from the rate the tub fills and you get your actual fill rate.

Now divide 100 by the actual fill rate and you get the answer in seconds.

I hope this helps.

your assuming hot and cold are coming out of separate spouts right?

[Quartz]

Originally Posted by kman

your assuming hot and cold are coming out of separate spouts right?

Yes I did.