A small grill can hold two hamburgers at a time. If it takes 10 minutes to cook one side of a hamburger, and 5 minutes to cook the other side, then what is the shortest time needed to cook both sides of three hamburgers?

15 minutes for 2

15 minutes for 1

Total 30 minutes

30

To find the shortest time needed to cook both sides of three hamburgers, we need to break down the cooking process step by step and consider the cooking time for each side.

We know that it takes 10 minutes to cook one side of a hamburger and 5 minutes to cook the other side. This means that for each hamburger, it will take a total of 10 + 5 = 15 minutes to cook both sides.

Since the grill can hold only 2 hamburgers at a time, we can cook two hamburgers simultaneously. Therefore, we will need to cook the hamburgers in two batches: the first batch with 2 hamburgers and the second batch with only 1 hamburger.

For the first batch:
- It will take 15 minutes to cook both sides of each hamburger, so it will take a total of 15 minutes to cook both sides of the 2 hamburgers in the first batch.

For the second batch:
- Since we can only cook 1 hamburger at a time now, it will take 15 minutes to cook both sides of the single hamburger.

Now, we add up the cooking times for both batches:

- For the first batch: 15 minutes
- For the second batch: 15 minutes

Therefore, the shortest time needed to cook both sides of three hamburgers is 15 + 15 = <<15+15=30>>30 minutes.