<PRE><B>Question 150822</B>
A tank can be filled by two pipes separately in 10 and 15 minutes respectively. When a third pipe is used simultaneously with the first two pipes, the tank can be filled in 4 minutes. How long would it take the third pipe alone to fill the tank?
:
Let x = time (in min) required by the 3rd pipe alone:
Let the full tank = 1
:
{{{4/10}}} + {{{4/15}}} + {{{4/x}}} = 1
:
Multiply equation by 30x to eliminate the denominators, results
3x(4) + 2x(4) + 30(4) = 30x
:
12x + 8x + 120 = 30x
:
20x + 120 = 30x
:
120 = 30x - 20x
:
120 = 10x
x = {{{120/10}}}
x = 12 min for the third pipe to fill it alone
;
:
Check solution using a calc
(4/10) + (4/15) + (4/12) = 
 .4 + .267 + .333 = 1
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