Question 711800
Let r = filling rate of the large pipe.

It takes the smaller pipe twice the time that the larger pipe takes to fill the pool.  


That means, filling rate for the small pipe is {{{(1/2)r}}}.


If water flows through both pipes it take 2 1/3 hours to fill the pool.

Both pipes open and filling the pool at the same time means that the fill rate is {{{r+(1/2)r}}}.  At this extent of information development, you could create a table of data but this is not really necessary.  You are given the time it takes to DO THE JOB of filling the tank, being {{{2&1/3}}} hours.


Pipe___________rate_______________time____________how many jobs
Small___________{{{r/2}}}_______________(____)___________1
Big_____________r_________________(____)___________1
Both Together___{{{r+(1/2)r}}}_____________{{{2&1/3}}}_____________1


If the rate is number of jobs per unit of time, and if time is time (be consistant with the unit you use), then rate multiplied by time is the number of jobs. r*t=j, using j as a variable for how many jobs.  Let's use those!


{{{highlight((r+r/2)(2&1/3)=1)}}}, we need to find r, the fill rate for the big pipe. Just algebra steps.  


Remember, r is in units of jobs per hour.  YOU want the reciprocal.  When you find r, calculate its reciprocal.  You want {{{1/r}}}, but easier first to find r.


post note:  In fact even if you check the previous tutor's solution you will find your arithmetic mistake.  A factor of 2 missing.  My work gave me {{{14/9}}} jobs per hour which is {{{9/14}}} hours to fill the pool just through the big pipe.  39 minutes.