Question

Liza can fill a bucket with water in 45 seconds. Unfortunately, Bob pokes a hole in it, so if initially full, the bucket, the bucket will now become empty in one minute. How long will it take to fill the bucket with the hole in it?

Answer 1

x = amount of fluid ounces

so, if Liza can fill it up in 45 seconds, that means that in 1 seconds she has done (1/45)x fluid ounces.

now the hole can drain it in 60 seconds or a minute, that means that in 1 second, the hole has drained (1/60)x fluid ounces.

now, if we just subtract Liza's rate from the Hole's, what's leftover is that rate at which the bucket is being filled up.


`\bf \stackrel{\textit{Liza's rate}}{\cfrac{1}{45}x}~~-~~\stackrel{\textit{Hole's rate}}{\cfrac{1}{60}x}~~~~=~~~~\cfrac{4x-3x}{180}\implies \cfrac{1}{180}x`

that means the bucket is filling up at (1/180)x fluid ounces per second, in order to get a "whole", that be 180/180, so namely if it's doing 1/180 in 1 second, it'll take 180 seconds to do the whole bucket, or 3 minutes.