Question

A pipe can empty tank in 12 minutes alone and in 8 minutes along with pipe y

Answer 1

1) If a pipe can empty a tank in 12 minutes that means:

i) After 12 minutes the tank will be fully empty - 1 whole or 12/12

ii) If this pipe empties 12/12 of the tank in 12 minutes, then in 1 minute the tank will be 1/12 empty.

2) If a pipe y can empty the same tank in y minutes:

i) After y minutes the tank will be fully empty - 1 whole or y/y

ii) If pipe y empties y/y of the tank in y minutes, then 1 minute the tank will be 1/y empty.

When both pipes empty the tank together, it takes 8 minutes

- then the fraction emptied by both = 1/8 of the tank

  The fraction filled by both pipes can also be expressed as:
   
          1/y + 1/12=   (12+y)/12y

Therefore:

(12+y)/12y = 1/8

8(12+y) = 12y

96 + 8y = 12y

96 = 12y - 8y

4y = 96

y = 96/4

y= 24

Therefore pipe y can empty the tank alone, in 24 minutes