Fill My Water Bucket !!!!!!

Algebra Level 3

I want to fill my bucket using both cold and hot water. I have two taps for both cold and hot water. The hot water tap fills the bucket in exact 6 hours and cold water tap fills the bucket in exact 4 hours. I turn both of them simultaneously but i forgot to turn off another tap which remove the water out of bucket. This tap can empty the bucket in 12 hours. How Long will it take to fill the bucket ?

The answer is in Hours ...


The answer is 3.

Karan Ahire by Karan Ahire , 21, India

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1 solution

Aryan Gaikwad
Feb 21, 2015

Water filled by hot tap in 1 hour = \frac { 1 }{ 6 } and water filled by cold tap in 1 hour = 1 4 = \frac { 1 }{ 4 }

Water emptied by the third tap in 1 hour = 1 12 = \frac { 1 }{ 12 }

If all of these taps work together, then water filled in 1 hour =

⇒ 1 4 + 1 6 − 1 12 ⇒ 4 12 ⇒ 1 3 \Rightarrow \frac { 1 }{ 4 } +\frac { 1 }{ 6 } -\frac { 1 }{ 12 } \\ \Rightarrow \frac { 4 }{ 12 } \\ \Rightarrow \frac { 1 }{ 3 }

Therefore, time required to fill the bucket is 3 3 hours.

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