You can survive more than 3 weeks without food, however water is a different story.
With your body being over 60% water and every living cell in the body needing it to keep functioning. 4-7 days is the accepted timeframe before your body starts to shut down Water acts as a lubricant for your joints, regulates your body temperature through sweating and respiration and helps to flush waste.
There is no magic amount of water that you need to drink, as it depends on a number of factors. As a general rule 1-1.5 litres is what you should be aiming for each day under normal conditions, if however you are functioning in hot humid conditions, are exercising, running or have been ill you should be drinking more, and if your running ultra distances probably a lot more. The other golden rule of running is to start early and make sure you sip on it regularly, because by the time you feel thirsty you are already becoming dehydrated and under extreme conditions you will struggle to rectify the situation.
I have in the past seen the effects of dehydration and in fact have had a DNF in a road ultra because of it, though the worst example I have witnessed, was an Olympic class athlete who ran for the same club as me, and was to represent the club in a 10k road event, but he was returning from racing overseas and his plane was delayed so he came straight from the airport to the start. Now traveling in a plane is a dehydrating factor but in his haste to get to the start he probably drank very little. Now the outcome of this was he was in a perfect position to win when with less than a km to go he felt dizzy, his legs gave out, and he collapsed by the side of the road and needed to be placed on intravenous fluids to rehydrate him. So it pays to keep hydrated.
There are alternatives to just drinking water if you struggle consuming large amounts of it, as I know some do.
EAT YOUR WATER.
Virtually all food has some water in it. Natural, whole foods have the highest water content, with fruit and vegetables containing 80 to 98 percent water. Eating vegetables such as cucumbers, tomatoes or celery, and fruits like watermelon with a meal or as a snack is one of the easiest ways to increase your hydration.
Watermelon contains 92% water and essential electrolytes such as, calcium, magnesium, potassium and sodium. All of which makes it the perfect food to consume during an event or as a post workout rehydration snack.
Cucumbers have a 96% water content and are a great balance of electrolytes such as calcium, magnesium, potassium and sodium. The mineral, silica, also found in cucumber is essential for healthy lubricated connective tissue, which includes muscles, tendons, ligaments cartilage and bone.
My preference for a snack is watermelon, which I consume pretty much on a daily basis, however I do know a young school age girl, who is not that interested when offered sweets, but will happily sit and snack on a plate of sliced cucumber when she feels the need.