SOLUTION: two pipes running simultaneously can fill a tank in 2 hours and 40 minutes. after the large pipe had run for 3 hours the smaller pipe was also turned on and the tank was full 40 mi

                        RATE

BIG PIPE               

SMALL PIPE                

Time smaller pipe takes, alone:  

Let L be the time (in hours) for Larger pipe to fill the tank alone, and
let S be the time (in hours) for Smaller pipe to fill the tank alone.

In one hour (in each hour) the larger pipe fills  of the tank volume. It is the rate of the larger pipe.
In one hour (in each hour) the smaller pipe fills  of the tank volume. It is the rate of the smaller pipe.
Working together, the two pipes fill  of the tank volume. (So, the combined rate is the sum of the rates of individual pipes.)
We are given that in  hours (=8/3 hours) the two pipes fill the tank working together. It means that
 =  = .     (1)
Next, working for 3 hours, the larger pipe fills  of the tank volume.
Also, in 40 minutes (= of an hour), two pipes working together fill  of the tank volume.
And these two volumes are the entire tank volume:

 +  = 1.    (2)

Due to (1), we can rewrite (2) in the form

 +  = 1,   or    +  = 1.

This is an equation to determine L, and you can easily solve it:   =    and   L = 4.
So, the larger pipe fills the tank in 4 hours.

Then from (1)   = ,    =   and  S = 8.

Answer. The smaller pipe fills the tank in 8 hours.