Why is it taking so long?

Algebra Level 2

I have a pipe, which can fill water in a beaker in 6 hours. But, there is a hole at the bottom of the beaker that can empty the same beaker which is full of water in 8 hours.

How much time (in hours) will the pipe take to fill the beaker. If the hole is also opened?

Assumptions: The beaker is to be assumed empty when the pipe and hole are opened to fill and empty it respectively. Water is flowing out at a constant rate, regardless of the depth of the water.

This question is part of the set All-Zebra

12 The beaker won't get filled. 6 18 24

1 solution

展豪張
Apr 29, 2016

The pipe fill $\dfrac 16$ of beaker in $1$ hour.
The hole empty $\dfrac 18$ of beaker in $1$ hour.
The net effect is $\dfrac 16-\dfrac 18=+\dfrac 1{24}$ per hour.
It takes $24$ hour to fill the beaker if both pipe and hole are open.

Yes, that's correct, have a look at this

Abhay Tiwari - 5 years, 1 month ago

You should probably state the assumption that water is flowing out at a constant rate , regardless of the depth of the water. In reality, the rate would depend on the water depth, ideally according to Torricelli's Law

Otto Bretscher - 5 years, 1 month ago

Thanks a lot, for the information. I will correct it.

Abhay Tiwari - 5 years, 1 month ago

Haha that's too difficult for me!

展豪張 - 5 years, 1 month ago

Why is it taking so long?

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