Question

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 will take 10 more minutes for the water to reach the top of the tub if it continues at the same rate. Is he correct. Explain

Answer 1

He is not correct for thinking it will take ten more minutes. It will take 12 more minutes.

If you get a piece of paper and my 18 hash marks (stands for the 18 inch depth of the tub) like this:

IIIIIIIIIIIIIIIIII

and you group them by 3 (standing for three inches):

III III III III III III

You would see that you have six groups of three. If it took two minutes to fill the first three inches, every three inches it fills will take two minutes. So if you multiply 2 x 2 x 2 x 2 x 2 x 2 you will get the answer 12.

Answer 2

Depth of the bathtub = 18 inches

Time taken to fill 3 inches of the bathtub = 2 minutes

Then

The amount of depth needed to fill with water = (18-3) inches

= 15 inches

Time required to fill 15 inches of the bathtub = (15*2)/3 minutes

= 30/3 minutes

= 10 minutes

So John is correct in thinking that it will take 10 more minutes for the water to reach the top of the tub if he continues at the same rate.

Hope this helps!