In order to figure this out, we need to create a picture.

Since bob is traveling south, and the current is traveling west, they are perpendicular to each other. This means that they are  to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Bob is actually going. 

Recall that the Pythagorean Theorem is , where  is the hypotenuse, and ,  are the legs of the triangle, and  have a  angle between them.

For our calculations, let , and . 

In order to figure this out, we need to create a picture.

Since Amanda is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are  to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed Amanda is actually going. 

Recall that the Pythagorean Theorem is , where  is the hypotenuse, and ,  are the legs of the triangle, and  have a  angle between them.

For our calculations, let , and . 

Since the rock is going in the opposite direction of Jack, we simply subtract the speed of the rock from how fast Jack is going down the hill. 

In order to figure this out, we need to create a picture.

Since the airplane is traveling south, and the wind is coming from the west, they are perpendicular to each other. This means that they are  to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed the airplane is actually going. 

Recall that the Pythagorean Theorem is , where  is the hypotenuse, and ,  are the legs of the triangle, and  have a  angle between them.

For our calculations, let , and . 

Since the coin is going in the same direction as Jill, we simply add the speed of the coin and how fast Jill is going down the hill. 

Since Bob's wallet is going in the opposite direction, we simply subtract the speed of the wallet from how fast Bob is going down the hill. 

In order to figure this out, we need to create a picture.

Since John is traveling north, and the current is traveling east, they are perpendicular to each other. This means that they are  to each other. The next step is to use the Pythagorean Theorem in order to solve for what speed John is actually going. 

Recall that the Pythagorean Theorem is , where  is the hypotenuse, and ,  are the legs of the triangle, and  have a  angle between them.

For our calculations, let , and . 

Since the rock is going in the same direction as Jack, we simply add the speed of the rock to how fast Jack is going down the hill. 

Since the airplane and the wind are going in opposite directions, we simply subtract the speed of the wind from the speed of the plane.

Since the airplane and the winds are going the same direction, we simply add the airplane and wind speeds together.