Harry started a 6-mile hike with a full 10-cup canteen of water and finished the hike in 2 hours with 1 cup of water remaining in the canteen. If the canteen leaked at the rate of 1 cup per hour and Harry drank 3 cups of water during the last mile, how many cups did he drink per mile during the first 5 miles of the hike?

We need to know how much he drank per mile in the first 5 miles. That is in 10/6 hours or 100 mins.

He started with 10 cups. Ended with 1 cup. Therefore total loss of water is 9 cups which has happened through various reasons.
If the canteen leaked at the rate of 1 cup/hour 2 cups of water would have leaked in 2 hours.
We now have 7 cups of water to account for.
If 3 cups of water were drank in the last mile 4 cups of water drank in the first 5 miles.

Therefore, she drank 4/5 cups per mile in the first 5 miles.