Question 550806
A reservoir can be filled by one pipe in 6 hrs and by another pipe in 8 hrs. It can be emptied by a third pipe in 10 hrs. Starting empty, how long will it take to fill the reservoir if all pipes are open?
<pre>

Let the time be x hrs to fill 1 reservoir, and fill in x for the time
and 1 for the number of reservoirs

Make this chart:
                       number of       time in        rate in
                       reservoirs       hours      reservoirs/hour
1st pipe alone              

2nd pipe alone

3rd pipe alone

All pipes together        1               x

Fill in the given times for 1st and 2nd pipes to fiil 1 reservoir.
But fill in -1 for the 3rd pipe because to drain 1 reservoir is the
same mathematically as "filling -1 reservoirs"

                       number of       time in        rate in
                       reservoirs       hours      reservoirs/hour
1st pipe alone            1               6  

2nd pipe alone            1               8

3rd pipe alone           -1              10

All pipes together        1               x

Now fill in the rates in reservoirs/hour by dividing reservoirs by
hours:

                       number of       time in        rate in
                       reservoirs       hours      reservoirs/hour
1st pipe alone            1               6            {{{1/6}}}
2nd pipe alone            1               8            {{{1/8}}} 
3rd pipe alone           -1              10           {{{-1/10}}} 
All pipes together        1               x            {{{1/x}}}

The equation is gotten by adding the rates of the first three and
setting that sum equal to the combined rate:

                        {{{1/6}}} + {{{1/8}}} - {{{1/10}}} = {{{1/x}}}  

Solve that and get {{{120/23}}} or {{{5&5/23}}} hours or 5.217391304 hrs.

Edwin</pre>