John is filling a bathtub that is 18 inches deep. He notices it takes 2 mins. To fill the tub 3 inches of water. He estimates it

The bathtub's depth measures 18 inches

It takes 2 minutes to fill 3 inches of the bathtub

Subsequently

The remaining depth needed for filling with water = (18-3) inches

                                                                        = 15 inches

The time needed to fill the remaining 15 inches of the bathtub = (15*2)/3 minutes

                                                                      = 30/3 minutes

                                                                      = 10 minutes

Therefore, John is right in believing that it will require an additional 10 minutes to fill the tub to the brim at the same rate.

Hope this clarifies things!

John's assumption about it taking ten more minutes is incorrect; it will actually take 12 minutes more.

If you use a piece of paper and make 18 hash marks (representing the 18 inches of the tub) like this:

IIIIIIIIIIIIIIIIII

and group them in sets of three (which represent each 3 inches):

III III III III III III

You would see that there are six groups of three. Since filling the initial 3 inches took two minutes, every subsequent three inches will also require the same time. If you multiply 2 by 2 for each group, you will arrive at the total of 12.