Answer:
To determine how far apart the bear and the gorilla will be at the end, we need to consider the distance each of them travels during the additional 20 minutes.
First, let's calculate the distance the bear travels. Since the bear travels at a speed of 10 mph, in 20 minutes (which is 20/60 = 1/3 hours), the bear will cover a distance of 10 mph * (1/3) hours = 10/3 miles.
Next, let's calculate the distance the gorilla travels. The gorilla travels at a speed of 20 mph. Since the gorilla leaves 12 minutes before the bear, the gorilla has a head start of 12/60 = 1/5 hours. Therefore, the gorilla will travel for a total of (1/5 + 1/3) = 8/15 hours. Multiplying this by the gorilla's speed of 20 mph, we find that the gorilla will cover a distance of 8/15 * 20 mph = 32/3 miles.
Now, we can determine the final distance between the bear and the gorilla. Since they are traveling in opposite directions, we need to add their distances together. Adding 10/3 miles to 32/3 miles gives us a total distance of (10/3 + 32/3) miles = 42/3 miles = 14 miles.
Therefore, at the end of the additional 20 minutes, the bear and the gorilla will be 14 miles apart.