Question From Readers # 4: How Long To Empty Tanks

How long will it take to empty it if the 3 pumps are working together

If a pump can empty a tank in 16 hrs, another pump can empty the same tank in 8 hrs, and another caempty this tank in 12 hrs. How long will it take to empty it if the 3 pumps are working together on this tank.

What is asked?

How long will it take to empty it if the 3 pumps are working together on this tank.

Analysis:

In this problem, it is not necessary to get or to know  the volume of the tank. So you can put any figure of volume of the tank - be it 1,000 or 10,000, the answer is the same.  

Solution:

Let us say the volume of the tank is 1000 cubic meter. 

We have to get the rate of each tank. 

Pump A        1000 ­m³ ­÷ 16 hr = 62.5 m³/hr

Pump B        1000 m³ ÷   8 hr = 125 m³/hr

PumpC        1000 m³ ÷ 12 hr = 83.33 m³/hr

                                                 270.83 m³/hr is the combined rate of 3 pumps

Now we have to divide the volume by the combined rate of 3 pumps.

                    1000 m³ ÷ 270.83 m³/hr = 3.69 hrs is the time for the 3 pumps to empty the tank.  

But if you want to solve this as it should be, I mean by letting X as the volume since it is unknown, so this is it.

Let x be the volume.

Pump A     x ÷ 16 =  x 

                               16

Pump B     x ÷ 8 =  x 

                              8

Pump C     x ÷ 12 =  x  

                               12

 x  + x  + x  = 3x + 6x + 4x  = 13x

16   8     12           48               48

Now, x ÷ 13x 

                48

     

 x  ÷  13x  

1       48   

x   x   48   = 48x  = 3.69

1       13x     13x 

If you find this helpful, please click the share button below to share this post to your friends. Sharing is caring...