SOLUTION: 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 reservoi

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: 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 reservoi      Log On


   

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?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
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            1%2F6
2nd pipe alone            1               8            1%2F8 
3rd pipe alone           -1              10           -1%2F10 
All pipes together        1               x            1%2Fx

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

                        1%2F6 + 1%2F8 - 1%2F10 = 1%2Fx  

Solve that and get 120%2F23 or 5%265%2F23 hours or 5.217391304 hrs.

Edwin