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 it take when all the four pipes are opened?
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Let the 4 pipes be: a, b, c, d
Let a full tank = 1
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"1,2,3 pipes are opened tank filled in 12 minutes"
{{{12/a}}} + {{{12/b}}} + {{{12/c}}} = 1
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"2,3,4 pipes are opened tank filled in 15 minutes"
{{{15/b}}} + {{{15/c}}} +  {{{15/d}}} = 1
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Multiply the 1st equation by 5, the 2nd equation by 4, results
{{{60/a}}} + {{{60/b}}} + {{{60/c}}} = 5
{{{60/d}}} + {{{60/b}}} + {{{60/c}}} = 4
-------------------------subtraction eliminates b and c
{{{60/a}}} - {{{60/d}}} = 1
then
"1,4 pipes are opened tank filled in 20 minutes"
{{{20/a}}} + {{{20/d}}}  = 1
multiply this equation by 3
add to the above equation
{{{60/a}}} + {{{60/d}}} = 3
{{{60/a}}} - {{{60/d}}} = 1
-----------------------adding eliminates d find a
{{{120/a}}} = 4
4a = 120
a = 120/4
a = 30 min when the pipe 1 fills it alone
then
{{{20/30}}} + {{{20/d}}} = 1
{{{20/d}}} = 1 - {{{2/3}}}
{{{20/d}}} = {{{1/3}}}
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
{{{12/30}}} + {{{12/(bc)}}} = 1
.4 + {{{12/(bc)}}} = 1
{{{12/(bc)}}} = 1 - .4
{{{12/(bc)}}} = .6
.6bc = 12
bc = 12/.6
bc = 20 min pipes 2&3 alone
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"How much time will it take when all the four pipes are opened?
{{{t/30}}} + {{{t/20}}} + {{{t/60}}} = 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"
{{{15/(20)}}} + {{{15/60}}} = 
.75 + .25 = 1






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