# Water fills the tub in 12mins, and empties the tub in 20min when the lid is open. How long will it take to fill an empty tub if the lid is open? Answer: 30min. How do I solve it?

##### 1 Answer
Mar 11, 2018

Suppose,the whole volume of the tub is $X$

so,during filling of the tub,

in $12 \min$ volume filled is $X$

so, in $t \min$ volume filled will be $\frac{X t}{12}$

For emptying,

in $20 \min$ volume emptied is $X$

in $t \min$ volume emptied is $\frac{X t}{20}$

Now,if we consider that in $t \min$ the tub must be filled,that means,voulme filled by tap must be $X$ amount larger than volume emptied by lead,such that the tub will be filled due to higher speed of filling and excess water will be emptied by the lid.

so, $\frac{X t}{12} - \frac{X t}{20} = X$

or, $\frac{t}{12} - \frac{t}{20} = 1$

so, $t \frac{20 - 12}{20 \cdot 12} = 1$

so, $t = \frac{20 \cdot 12}{8} = 30 \min$