During the last drought, the water table dropped so low that three villages in the plains ran out of drinking water. The council organised a light duty tanker to carry water from the main reservoir to the villages on a weekly basis.
At the start of each trip the tanker was always full of water; unknown to the driver, just as he started driving from the reservoir, the water tank developed a leak. By the time he reached the first village, the tanker had lost half of the water from the water tank and consumed half of the fuel tank. You can assume that the fuel consumption of the truck is directly proportional to the weight it carries, and that the water flow (in the leakage) and the speed of the truck were constant for the whole journey.
We also know that an empty tanker uses exactly one sixth of the fuel tank when travelling from the first village back to the reservoir.
Disregarding the fuel tank weight, what fraction of the fuel tank would be spent to reach the first village when the truck had no leak?
