Word Problem HELP?

Question

Santa Claus is stuck in a chimney that is 10 feet long. At night he goes down 3 feet and by day he goes up 2 feet. How long will it take Santa to go down the chimney and deliver the presents?

Answer 1

Let's assume Santa arrived at night, and got stuck at the exact top.

First, let's model day 1: Santa starts at 10 ft. That night, he goes down 3 feet. The next day, he goes up 2 feet, leaving him at 9 feet up the chimney.

Now, we need to decide when Santa reaches the bottom. Since Santa goes down 3 feet at night, he'll reach the bottom on the night where he starts 3 feet up the chimney.

Now that we have determined his net drop per day (1 ft/day), and the point at which he reaches the bottom (he needs to travel 7 feet before the point where he'll slide down 3 feet to the bottom), we can determine that he will be stuck for 7 full days and the remaining night.