12mins to fill bath by hot tap 15mins by cold tap 20mins by shower. How long to fill if all 3 turned on.?

Answer 1

Let bath capacity be X litres
Hot tap rate = X / 12 litre / min
Cold tap rate = X / 15 litres / min
Shower tap rate = X / 20 litres / min
Fill rate = X / 12 + X / 15 + X / 20 litres / min
Fill rate = (5X + 4X + 3X) / 60 litres / min
Fill rate = 12X / 60 = X / 5 litres / min.
t = X / (X / 5) min
t = 5 min
Will take 5 min. if all three turned on.

Answer 2

First of all think about the answers you are listing here. I have seen 18 to 15.5 minutes. If you think about this, how can the sum of all three have a slower time then two of the single filling times.

We first have to assume that the cold water, hot water and shower have no direct pressure connection and run off of three separate sources. If this assumption is not made then there is not enough information to solve.

Since the size of the tub is not given I will make up a unit called T and it will equal one tube unit. I will now assign a rate to each tap. The cold water takes 12minutes/tub The hot takes 15minutes/tub and the shower takes 20minutes/tub.

Now I want to find out how long it takes all three of them to fill one tub.

My formula for the cold water would: 12min/T = 1 or T = 12minutes or (1/12)T = 1minute

I can do the same for the hot and the shower.

(1/15)T = 1 minutes for the hot
(1/20)T = 1 minute for the shower

If I add them all together I would get:

(1/15) + (1/12) + (1/20) = 1/T

1/T = 0.2 or T = 5 minutes

*seems that someone got it in their head that 7 is the correct answer based on a "Guess" and everyone ran with it throwing out mathematics and keeping their assumptions to themselves.*

Answer 3

I'd educate a guess at 7 minutes. Usually the shower will be plumbed into the cold water supply so that would reduce the pressure from the cold tap...so forget the shower.

It can't be more than 12 minutes because the hot tap alone will do the job in that time. It can't be less than six minutes as it takes the cold tap 7.5 minutes to fill half the bath. Bearing in mind the hot tap is the fastest, then filling the bath should take between 6.5 and 7.5 minutes.

Answer 4

Well each would fill 1/3 of the bath,

so 1/3 of 12 = 4 mins
so 1/3 of 15 = 5 mins
so 1/3 of 20 = 6.66666 Mins

So I would say 15.66 So About 15 and A half minutes :)

Answer 5

in 1 hour
hot tap fills 5 bath
cold tap fills 4
shower fills 3

so in 60 minutes, all 3 fill 12 bath-tubs
you want 1, so 60/12=5 minutes
that's neglecting water pressure and assuming each have it's own source of water/tank or whatever.

Answer 6

is the shower a seperate tap ?
or using the hot and cold if it is it will fill in 20min

the fastest filling is 12 by hot adding cold would 1/2 it and adding shower would 1/3 it im saying 4 mins

Answer 7

7

Answer 8

5 minutes is my answer, negating water pressure and all points being seperate.

If you make the bath an arbitrary size i.e 60 units.
Then the hot tap fills at a rate of 5 units per min
The cold tap fills at a rate of 4 units per min
The shower fills at a rate of 3 units per min

That results in total for all three is 12 units per min.
To fill the original bath would require 5 minutes.

The original size is arbitrary as long as it is a constant applied throughout.

**wonder who's just giving random thumbs down, what's the point in that?**

Answer 9

five minites, its no guess!

If the baths 100L flow rates are as follows Liters/minite
hot 25/3
cold 20/3
shower 5

added together is 20L/min so therefore 5 minites

I pity the pepole who think that each tap/shower will fill a 1/3 up.

Answer 10

why are people giving neagative replies to people saying 5 mins, they are 100% correct. If the assumption regarding water pressure is made (and it needs to be to get an answer) then the time to fill will be 5 mins.