Suppose it takes 18 hours for a pipe to fill a tank of water, if the tank had no leak. However, our tank has a crack that will cause a full tank to
leak out in 30 hours. If the tank starts off empty, how long will it take to
fill the leaky tank?

Step-by-step explanation:

Let the volume of tank be x

In 18 hours volume of tank filled = x

we have to find the volume of tank which is filled in 1 hours.

For that we divide LHS and RHS by 18

In 18/18 hours volume of tank filled = x/18

In 1 hours volume of tank filled = x/18

In 30 hours volume of tank emptied = x

we have to find the volume of tank which is emptied in 1 hours.

For that we divide LHS and RHS by 30

in 30/30 hours volume of tank filled = x/30

In 1 hours volume of tank filled = x/30

If tank is empty and one starts to fill it, two things will happen

it will start filling at rate of x/18 hours

But there is leak which will start to empty the tank at  x/30 hours

So , at any given time rate if filling of water will be rate of filling the tank- rate of emptying the tank

In 1 hour volume of tank filled if both filling and leaking takes place simultaneously =  x/18 -x/30 = (30-18)x/18*30 = 12x/18*30 = x/3*15 = x/45

In 1 hour volume of tank filled = x/45

in 1*45 hour volume of tank filled = x/45*45 = x

Thus, it will take 45 hours to fill the leaky tank  .

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.