Question 1074607
Consider the speed/rate with which the pipes can fill the pool,
in pool-fuls per hour.
For example, if a pipe can fill the pool in 10 hours,
its flow rate or pool-filling speed is {{{1/10=0.1}}} pool-fuls per hour.
 
So, if the rates of A, B, and C are {{{x}}} , {{{y}}} , and {{{z}}} respectively,
the rates add up to give you
{{{x+y=1/14}}} , {{{y+z=1/20}}} , and {{{x+z=1/16}}} .
All 3 equations together for a system of linear equations that you could solve.
Once you knew {{{x}}} , {{{y}}} , and {{{z}}} ,
calculate {{{x+y+z}}} , the rate for the 3 pipes together,
and from there calculate {{{1/(x+y+z)}}} ,
the time to fill the pool with all 3 pipes.
However, adding up the 3 equations, you get
{{{x+y+z=1/14×1/16+1/20}}} <---> {{{2(x+y+z)=103/560}}} <---> {{{x+y+z=103/(2*560)=1/1120}}}
and the time needed to fill the pool using all 3 pipes at once is
{{{1/(x+y+z)=highlight(1120/103)}}}{{{hours=about}}}{{{highlight(10.8738)}}} hours.
That is about 10 hours, 52 minutes, 26 seconds.
(The exact calculation cones to 
10 hours, 52 minutes, 25 and 65/103 seconds.