Suppose that, on average, a certain binary search algorithm takes one second to search through 1,000 items. Approximately how long will this algorithm take to search through 4,000 items?

4 seconds

Explanation:

If the binary search algorithm takes one second to search through 1000 items then, to get the time taken to search through 4000 items should be one second multiplied by 4.

Since

1000 items = 1 second

4000 items = y

-we cross multiply, we have

1000 items x y = 4000 items x 1 second

-divide both sides by 1000 items to obtain the value of y, we have

y = (4000 items x 1 second) / 1000 items

y = 4 seconds.