#2           61. TIME AND TIDE                  
Ashley and Herbert were having their weekly puzzle competition.

“Look,” said Ashley, “we have these two jars of the same size. In the first there is one amoeba. In the second jar there are two amoebas. An amoeba can reproduce itself in three minutes. Now if it takes two amoebas in the second jar three hours to fill the jar right up, how long does it take the one amoeba in the first jar?”

“What a novel problem!” cried Herbert delightedly. “But I know the answer. Perhaps you know this one?”

“A ship is at anchor. Over its side hangs a rope ladder with rungs 30 centimetres apart. The tide rises at the rate of 40 centimetres an hour. If the ladder has 24 rungs above the water level before the tide begins to rise, how many rungs will be above water after six hours?”
 Hints and strategies 

Hint                         Solution                      Extensions
HINT

Each of these problems has avery simple solution.

In the first problem, you might think about how long it takes for the single amoeba to double the population.

In the second, think about the physical situation with the ship and its ladder floating in the water.
HINT 2

You should have obtained remainders 6, 3, 7 for the respective departments. Also remainders 3, 2, 2, 2, 5 for F (Foster), K, P, R and W; all other names have remainder 0. You should now immediately be able to place five people in their departments.
SOLUTION

Since after three minutes we have two amoebas in the first jar, the answer is three hours three minutes.

The answer to the second problem is 24 rungs – the ship rises with the tide.
EXTENSION

1. The amoeba problemis really about powers. In unit time, population P doubles to 2P. So in time t, population P grows to 2tP. Notice how this relates to the answer to the problem. Look up exponential growth.

2. The ship problem is rather a trick question. One might say it is based on the theory of relativity!