A pipe can empty tank in 12 minutes alone and in 8 minutes along with pipe y
Answers
Answered by
2
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
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
Similar questions
English,
7 months ago
Math,
7 months ago
Political Science,
1 year ago
English,
1 year ago
Math,
1 year ago