Stranded on a deserted island, Harry Puttar is left with only a 30 litres container of milk. To conserve his milk he decides that on the first day he will drink one litre of milk and then refill the container back up with water. On the 2nd day he will drink 2 litres and refill the container. On the 3rd day he will drink 3 litres and so on... By the time all the milk is gone, how much water has he drunk?(1 Marks)
Question
Stranded on a deserted island, Harry Puttar is left with only a 30 litres container of milk. To conserve his milk he decides that on the first day he will drink one litre of milk and then refill the container back up with water. On the 2nd day he will drink 2 litres and refill the container. On the 3rd day he will drink 3 litres and so on... By the time all the milk is gone, how much water has he drunk?(1 Marks)
Solution
To solve this problem, we need to understand that each day, Harry is drinking a mixture of milk and water, but the proportion of milk in the mixture is decreasing.
On the first day, Harry drinks 1 litre of pure milk. The container is then refilled with water, so it contains 29 litres of milk and 1 litre of water.
On the second day, Harry drinks 2 litres of the mixture. Since the mixture is 29 parts milk and 1 part water, he drinks 1.93 litres of milk and 0.07 litres of water. The container is then refilled with water, so it contains 27.07 litres of milk and 2.93 litres of water.
On the third day, Harry drinks 3 litres of the mixture. Since the mixture is 27.07 parts milk and 2.93 parts water, he drinks 2.77 litres of milk and 0.23 litres of water. The container is then refilled with water, so it contains 24.3 litres of milk and 5.7 litres of water.
This process continues, with the proportion of milk in the mixture decreasing each day.
To find out how much water Harry has drunk by the time all the milk is gone, we need to add up all the water he drinks each day. This involves a series of calculations similar to the ones above.
However, without knowing how many days it takes for all the milk to be gone, we cannot give a specific answer. The number of days would depend on the exact proportions of milk and water Harry drinks each day, which are not specified in the question.
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