I found this question in a magazine.I know the ansewr but dont know the explanation.?

Question

A tap fills a bucket in 20mins. Another tap fills the same bucket in 30mins. So how long will it take if both the taps are running to fill the bucket? The answer is 12mins or something.
How to work this one out?

Answer 1

Ok heres the deal. Apply any size you want to the bucket since theyre filling the same one....it can be any number. I'll use 30. So the tap that fill it in thirty minutes pours one gallon per minute. 30 gallons divided by 30 minutes. The other tap fill the 30 gallons in 20 minutes. 30 dived by 20 it 1.5 gallons per minute. So add the two together and you get a combined 2.5 gallons per minute. Divide 30 by 2.5. You get 12

Answer 2

We just learned how to do this in math hold on. Let me solve this.
Let n=time it takes both taps to fill the bucket
Worker R x T = Part of job done
1st tap 1/20 x n = n/20
2nd tap 1/30 x n=n/30

60 n n 60 60
- + - = 1
20 30
3n+2n=60
5n=60
n=12 minutes

Answer 3

the 20 min tap will fill half the bucket in 10 mins
the 30 min tap will fill the other half in 15 mins
10 + 15 = 25mins
half of 25 is 12.5 mins.
if you filled it halfway with one tap then went to the other tap, it would take 25 mins. But since both taps are running into it at the same time, you divide the time in half.

Answer 4

This is what I'm thinking...

Two of the first tap would fill the bucket in 10 minutes. Two of the second tap would fill the bucket in 15 minutes. (For those you just cut the time in half because you exactly doubled the amount of water going in). Since you have one of each, you can average those two times and get 12.5 minutes.

Answer 5

you just have to use some algebra for this one.

let v=volume of bucket
sa=speed of 20min tap
sb=speed of 30min tap
t=time

using the forumla v=s*t and the information given, we can obtain the following 2 formulas (working in mins)

v=sa*20-------------------1
v=sb*30-------------------2

equate to obtain
sa*20=sb*30
sa=1.5sb---------------3

the question wants us to work out:
t=v/(sa+sb)
Subs in equ 3:
hence t=v/(1.5sb+sb)
t=v/(2.5sb)

substituting in equation 2 from before
t=(sb*30)/(2.5sb)
(now the sbs cancel out)
t=12 mins

hope that helps :D im not sure averaging gives you the correct answer so this is the way i go. the 2 different taps will not fill half the bucket each because they are going to give out different amounts so you can't halve it i dont think

Answer 6

You add together the time each tap takes to fill a bucket
as 1/2 of the filling
20 min--1/2==10
30mim--1/2 =15
----------------------
the 1/2 is equal to 25 then divide by 2 you will get

12.5

Answer 7

The average = 25.
Because you have two taps running, divide it by two.
25/2 = 12.5 minuts.

Answer 8

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Answer 9

well isnt that a mighty fine question.. why dont you write to the magazine you got it out of and ask for the explination.

Answer 10

Do your own homework!!