Question

Ok, imagine a large empty bin. Say that each minute people would come and put in one golf ball a piece. The first minute(Starting at 12 noon), 1 person came and put in a ball. The second minute, 2 people put in one ball a piece. A minute later, 4 people put in 1 ball a piece. A minute later, 8 people put in 1 ball a piece. This pattern continues until the bin was exactly full at 6 pm. At what time was the bin half empty?

Answer 1

At 5:59 the bin was half empty.

Explanation:

Consider the provided information.

The first minute(Starting at 12 noon), 1 person came and put in a ball. The second minute, 2 people put in one ball a piece. A minute later, 4 people put in 1 ball a piece. A minute later, 8 people put in 1 ball a piece. This pattern continues until the bin was exactly full at 6 pm.

Here we can observe that each minute the number of balls get double.

It is given that at 6 pm the bin was exactly full.

Let the number of balls at 6 pm was x.

Then the number of balls at 5:59 must be
`(x)/(2)`

Because the double of x/2 is x. Which is the capacity of bin.

Therefore, at 5:59 the bin was half empty or we can say that half full.