Two people meet in the purple room on the fourth floor of a building. on departure, one person travels west 16 feet, south 9 feet, and down 9 feet. the other person travels north 16 feet, east 8 feet, and up 9 feet. how far apart are the two people?

To solve this word problem, I am going to first look at what I know.
1) They are in the purple room on the fourth floor of a building.
2) We know that they went separate ways. 
Person 1:
Travels west 16 feet. So this person traveled left 16 feet and is on the same floor.
Travels south 9 feet. This person traveled down 9 feet.
Travels Down 9 feet. Travels down again at 9 feet.
Person 1 went to the left 16 feet and down 18 feet from starting point in the purple room. 
Person 2:
Travels North 16 feet. Travels up 16 feet.
Travels East 8 feet. Travels right 8 feet. 
Travels up 9 feet. Travels up 9 feet. 
The person on went up 25 feet and to the right 8 feet.
Now, we are going to subtract the opposites from each person (left, right) (up, down)
Equation 1 looks like this: 25-(-18) The 18 is negative because person 1 went down from starting point. - and - equals a positive. So, 25+18= 43
Equation 2 looks like this: (-16)-8 The answer is 24 feet.
So, they are 43 feet away from each other vertically and 24 horizontally. 
Hope this helps!