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?
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
2nd pipe alone 1 8
3rd pipe alone -1 10
All pipes together 1 x
The equation is gotten by adding the rates of the first three and
setting that sum equal to the combined rate:
+ - =
Solve that and get or hours or 5.217391304 hrs.
Edwin