Question 550223: out of four pipes when 1,2,3 pipes are opened tank filled in 12 minutes; when 2,3,4 pipes opened time taken is 15 minutes;when 1 and 4 are opened it taken 20 minutes. How much time will take when all the four pipes are opened?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! out of four pipes when 1,2,3 pipes are opened tank filled in 12 minutes;
when 2,3,4 pipes opened time taken is 15 minutes;
when 1 and 4 are opened it taken 20 minutes.
How much time will it take when all the four pipes are opened?
:
Let the 4 pipes be: a, b, c, d
Let a full tank = 1
:
"1,2,3 pipes are opened tank filled in 12 minutes"
 +  +  = 1
:
"2,3,4 pipes are opened tank filled in 15 minutes"
 +  +  = 1
:
Multiply the 1st equation by 5, the 2nd equation by 4, results
 +  +  = 5
 + + = 4
-------------------------subtraction eliminates b and c
- = 1
then
"1,4 pipes are opened tank filled in 20 minutes"
 +  = 1
multiply this equation by 3
add to the above equation
+ = 3
- = 1
-----------------------adding eliminates d find a
 = 4
4a = 120
a = 120/4
a = 30 min when the pipe 1 fills it alone
then
 + = 1
= 1 - 
= 
d = 3*20
d = 60 min when pipe 4 fills it alone
:
Let's treat pipes 2&3 as a single pipe, call it bc
 +  = 1
.4 + = 1
= 1 - .4
= .6
.6bc = 12
bc = 12/.6
bc = 20 min pipes 2&3 alone
:
"How much time will it take when all the four pipes are opened?
 +  +  = 1
multiply by 60
2t + 3t + t = 60
6t = 60
t = 10 minutes all pipes together
:
:
see if this checks out using the 2nd original equation
"2,3,4 pipes are opened tank filled in 15 minutes"
 +  =
.75 + .25 = 1
:
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