A marine biologist is checking on the health on a sea coral reef. She begins 3 feet above the surface, then dives down 12 feet. She decides to investigate a manta ray and dives another 17 feet. Next, she notices a reef shark and swims up 22 feet. She spots a sea star patch and dives down another 13 feet to reach it. At what depth is she now swimming?

She is now swimming right at 17 feet below the surface.

Step-by-step explanation:

In this kind of problems, involving directions, etc, usually one position is the positive direction and the other position is the negative direction.

In our problem, we suppose that the surface is the positivo zero, above the surface is the positive position (positive depth) and below the surface is the negative directions (negative depth).

The problem states that the marine biologist begins 3 feet above the surface, so her initial position is + 3 feet.

Then, she dives down 12 feet. Diving down means diving in the negative direction, so her depth is now 3-12 = - 9 feet. Now, she is 9 feet below the surface.

It is following by another dive of 17 feet. It means that her depth is now - 9-17 = - 26 feet. She is now 26 feet below the surface.

Then, she swims up 22 feet. Swimming up means swimming in the positive direction, so her depth is now - 26+22 = - 4feet. Now, she is 4 feet below the surface

Finally, she dives down another 13 feet. Diving down means diving in the negative direction, so her depth is now - 4-13 = - 17 feet. She is now swimming right at 17 feet below the surface.