Henry got thirsty and drank 1/2 the water in his canteen. Later, he drank 1/3 of what remained, etc. Mortimer, with a canteen of the same size, drank 1/2 the contents on the first drink, 1/2 of what remained on the second drink, etc. After each took 10 drinks, the water Henry had left was how many times greater that the water Mortimer had left?

Julia: Let s be the size of the canteen. Water left in H's canteen after 1 drink is s(1/2). After his second drink, the water left in his canteen is s (1/2) - [s (1/2)(1/3)] = s (1/2)(2/3) = s (1/3). Continuing, the water in H's canteen after tenth drink is s (1/11). See the pattern? If not, try H's THIRD drink. You will see the pattern. M's canteen has the same size s. Water left in M's canteen after 1 drink is s (1/2). After his second drink, the water left is s (1/2) - [s(1/2)(1/2)] = [s (1/2)^2]. Continuing, the water left in M's canteen after the tenth drink is s (1/2)^10. The ratio of H's remaining water to that of M's is [s (1/11)] / [s (1/2)^10] = (1/11) / [(1) / (2^10)] = 2^10 / 11. Huge number. Dr. G.