Sorry, you don't have it set up right.  The other tutor just assumed you had.

Your words "The fast pipe is an unknown (f)" shows you need to think harder
about what you are asked to find.  Don't say "a pipe is an unknown".  That's
not clear.  A pipe is not "an unknown". "Whatever you're looking for" is what
you must let be the unknown.

So look at what you are asked or told to find. You are looking for the
TIME for the slow pipe.  So let the slower pipe's TIME be t.  This works just
like 

Distance = Rate x Time 

except that "Number of pools filled" (which is usually 1, as it is in this
case) takes the place of "distance".

Start with this chart, putting in t for the time the slower pipe will
take and 1 for the number of pools it is to fill:

                         Number of
                        pools filled    rate          time
slower pipe alone            1                         t
faster pipe alone                      
both pipes together          


Now fill in the rate for the slower pipe alone, which is just like 
Rate = distance/time, this is (number of pools filled)/time, or
1/t for the rate of the slower pipe.

                         Number of
                        pools filled    rate          time
slower pipe alone            1           1/t           t
faster pipe alone                      
both pipes together          

Now since the faster pipe's rate is 1.25 faster than the slow
pipe's rate, multiply the rate of the slower pipe, 1/t, by 1.25, 
getting 1.25/t and put that for the faster pipe's rate.  You
don't need to fill in anything else for the faster pipe, for
it's not mentioned as filling the pool, just that it's 1.25 faster.

                         Number of
                        pools filled    rate          time
slower pipe alone            1           1/t           t
faster pipe alone                      1.25/t   
both pipes together         

Now you're told that when both pipes are open, the pool gets filled
in 5 hours, so put 1 for the number of pools filled when both pipes
are open together, and 5 for the time:

                         Number of
                        pools filled    rate          time
slower pipe alone            1           1/t           t
faster pipe alone                      1.25/t   
both pipes together          1                         5

Now put in the combined rate for both pipes together, which again, 
is just like Rate = distance/time, this is (number of pools filled)/time,
or 1/5 for their combined rate:

                         Number of
                        pools filled    rate          time
slower pipe alone            1           1/t           t
faster pipe alone                      1.25/t   
both pipes together          1           1/5           5

So the equation is:

Slower pipe's rate + Faster pipe's rate = their combined rate:

           

The LCD is 5t

          

          

          

So it would take the slower pipe 11 hours and 15 minutes to
fill the pool. 

Edwin