Final answer:
Kyle drank a total of 39/35 liter of water during the first half of the game.
Step-by-step explanation:
To find the amount of water Kyle drank during the first half of the game, we need to calculate the difference between the initial amount of water and the amount left at the end of the second quarter.
Let's assume Kyle's bottle initially held 1 liter of water.
At the end of the first quarter, he drank 5/7 of the bottle or (5/7) * 1 = 5/7 liter of water.
After the coach filled up his bottle during the second quarter, the bottle was full again.
At the end of the second quarter, he drank some more water and left only 2/5 of water in the bottle, which is (2/5) * 1 = 2/5 liter of water.
Therefore, Kyle drank a total of 5/7 + 2/5 = 25/35 + 14/35 = 39/35 liter of water during the first half of the game.