What's the formula for how long it takes to fill something up?

Also, can somebody point me in the right direction for the problem below? Please don't give me a solution, though.

During a rainstorm, an empty bucket moving up with vertical speed V gets filled in 2 minutes. The same bucket moving down with the same vertical speed V gets filled in 8 minutes. How long will it take to fill a motionless bucket?

I'm thinking five minutes but I'm not sure.

Guest Apr 3, 2018

#1**+2 **

Let d = bucket volume per unit area

Let u be rain velocity (positive downwards)

Bucket going up: d = 2(u + V). (1)

Bucket going down: d = 8(u - V). (2)

Bucket stationary: d = t(u + 0). (3)

Eliminate V from (1) and (2) to get u in terms of d, then substitute u into (3) and rearrange to get t.

Alan
Apr 3, 2018