Question 715261
"Fill the pool" is 1 job.


Pipe_____________rate______________time_______________jobs
Pipe One_________(____)____________7__________________1
Pipe Two_________(____)____________9__________________1
Both Pipes_______(_____)__________(___)_______________1


Fill in the missing information.  r*t=j, meaning r=j/t.


Pipe_____________rate______________time_______________jobs
Pipe One_________(1/7)____________7__________________1
Pipe Two_________(1/9)____________9__________________1
Both Pipes_______(1/7+1/9)__________(___)_______________1


RATE means how many jobs per hour.  The combined rate of both pipes together only needs to be computed from the sum.


Combined Rate, {{{1/7+1/9=(9+7)/63}}}
={{{highlight(16/63)}}} JOBS PER HOUR.


What the question asks is how many hours to do the job which is to "fill the pool."  We just need the reciprocal of this combined rate. That is {{{highlight(63/16)}}} hours.