Question 666302
We start by turning the times into rates.  
  
A pipe can fill the swimming pool in 15 hours, so the rate for the pipe is {{{1/15}}} of a swimming pool per hour.
 
A hose can fill the swimming pool in 23 hours, so the rate for the hose is {{{1/23}}} of a swimming pool per hour.
 
Their combined rate, r, is {{{1/15 + 1/23}}} of a swimming pool per hour.
{{{r = 1/15 + 1/23}}}
{{{r = (23/23)(1/15) + (15/15)(1/23)}}}
{{{r = 23/345 + 15/345}}}
{{{r = (23 + 15)/345}}}
{{{r = 38/345}}} of a swimming pool per hour
 
So both the pipe and the hose together will take {{{345/38 = 9&3/38}}} hours to fill the pool, or 9 hours 4 minutes and 44.21 seconds.