Question 1204617
A tub can be filled with hot water in 15 minutes, or with cold water in 12 minutes. The tub can also be emptied when the plug is pulled out, in 10 minutes. Farley ran the hot water in his tub for 6 minutes, then both the cold and hot water together for 3 minutes, and then with the two taps still running, he accidentally pulled the plug. How long did it take, in minutes, for the tub to fill after the plug was pulled?

A tub can be filled with hot water in 15 minutes,
it fills 1/15 of tub in 1 minute 
 Farley ran the hot water in his tub for 6 minutes,
6/15 of the tub was filled with hot water

  with cold water fills  in 12 minutes. 
it fills 1/12 of tub in 1 minute cold water


then he ran both the cold and hot water together for 3 minutes,
In 1 minute both taps on 1/12 +1/15 of the tub is filled= 9/60 = 3/20
In 3 minutes they fill 9/20 of the tub

Total water in tub = 6/15 + 9/20 = 51/60 

Balance to be filled = 1-51/60 = 9/60 of the tub



In 1 minute both taps on 1/12 +1/15 of the tub is filled= 9/60 = 3/20


 emptied when the plug is pulled out, in 10 minutes
drains 1/10 of tub in 1 minute

When both taps and drain are on it will fill
3/20-1/10 = 1/20 of the tub

1/20 of tub is filled in 1 minute
9/60 in how many minutes

(9/60) /(1/20)= 3 minutes