Your Nemesis: V.A.L.A.

You successfully set up cameras in the dwarf island bear cave and took the poachers rubber boat to escape the island. However, when you got to the ship anchored off shore, you now see that it is your dreaded nemesis, V.A.L.A., who is behind the attempt to get the bears.

When you are 1 km away from the ship, you see the captain start pulling up the anchor.  He has seen you in the raft, and he's trying to escape! Fortunately, you are going at 25 kph and it takes 3 minutes to raise the anchor so you have plenty of time to reach the boat before it takes off. Unfortunately, the girl standing on the bow jumps into the water and starts swimming towards your raft—she must be a hostage trying to escape! But if you pick her up, will you still have time to reach the boat? She is swimming toward you at 5 kph, you will lose 15 seconds to slow down and pull her into the boat, and the boat will only go 15 kph after you pick her up. Should you save the girl or leave her for the sharks?

Infrared Cameras

Congratulations, your plan worked! The mama bear chased after its missing cub and ran into the poachers just as you passed them. You didn't stick around to see the carnage, but from what you heard, you know that the angry bear has taken care of the poachers.

Before leaving the island in the poachers' boat, you want to set up infrared cameras in the cave to study the dwarf island bears. You want to place the cameras at even intervals throughout the 500 m long tunnel. You have 10 cameras and 2000 m of cable. If each camera needs a single length of cable connected to your computer at the entrance, how many cameras can you set up inside the cave? Note that you will have one camera all the way at the end of the tunnel but you can use the camera built into the computer for the entrance.

Hint:  If you type "sum n/x (n=1 to x)" into Wolfram Alpha you get this very useful equation: