Hours required

[Deepthi Subbu]

A cylindrical water tower with radius 5 m and height 8 m is 3/4 full at noon. Every minute, .08Ï€ m3 is drawn from tank, while .03Ï€ m3 is added. Additionally, each hour on the hour, there is a periodic drain of 4Ï€ m3. From noon, how many hours will it take to drain the entire tank?

[ashis979]

Volume of the tower = π5²*8m³ = 200π³
Since it's 3/4 full, amount of water in it = 200*(3/4) = 150πm³

Two things happening:

1. Every minute you are draining (0.08-0.03) = 0.05πm³ of water
Therefore, every hour you are draining 60*0.05 = 3πm³ of water
2. Every hour you drain an additional 4πm³ of water

So, each hour the total drainage is 7πm³ of water

To drain the entire tower it will take you 150/7 hours = 21 3/7 hours or appx 21 hours and 26 minutes.

[jaxis]

Volume of the tower = π5²*8m³ = 200π³
Since it's 3/4 full, amount of water in it = 200*(3/4) = 150πm³

Two things happening:

1. Every minute you are draining (0.08-0.03) = 0.05πm³ of water
Therefore, every hour you are draining 60*0.05 = 3πm³ of water
2. Every hour you drain an additional 4πm³ of water

So, each hour the total drainage is 7πm³ of water

To drain the entire tower it will take you 150/7 hours = 21 3/7 hours or appx 21 hours and 26 minutes.

i agree till 'each hour the total drainage is 7πm³ of water' part..

But after this.


total volume = 150πm³

So at 7 πm³ rate 147 πm³ will be drain in 21 hours. But the remainng 3 πm³ will also take 1 hour(because the other drain of 4 πm³ hppens only at the end of the hour) to drain. So, total time wil be 22.

[ashis979]

Oh you're right jaxis! Completely forgot about the adding and draining that's going on every minute for the last part.
Been a while...thank god I don't have to worry about the gmat anymore!