Task No. 1.1

## Condition:

On the potion-making exam, each student at Hogwarts School had to brew 4 potions. Hermione managed to complete the task in half an hour, Harry in 40 minutes, and Ron took 1 hour. How many potions would Ron, Hermione, and Harry brew together in 2 hours if they continued working at the same speeds?
# Answer: 36

## Exact match of the answer -1 point

## Solution.

Let's calculate the potion-making speed of each of the three students, measured in potions per hour. Hermione made 4 potions in half an hour, so in one hour she would make twice as many potions, which is 8. Therefore, her speed is 8 potions per hour. Harry made 4 potions in 40 minutes, which means 1 potion every 10 minutes, so in 60 minutes he would make 6 potions, giving him a speed of 6 potions per hour. As for Ron, he made 4 potions in one hour, so his speed is 4 potions per hour. Now, let's assume the three students work together for one hour. Hermione would make 8 potions in this hour, Harry would make 6, and Ron would make 4, so together they would make $8+6+4=18$ potions in this hour. Therefore, if they work together for 2 hours, they would make twice as many potions, which is $18 \cdot 2=36$ potions - giving us the desired answer.