Hey all, I am currently writing a paper on how algebra does not always have to be boring and that there are many problems that can be out of the box and challenging. My paper deals with five or so problems and how to solve them. Right now I am suck on two problems. Maybe someone could shed some light on these for me??? lol I am starting to run out of scrap paper.

1. if abc=1 and 1/a+1/b+1/c=a+b+c verify that at least one of a, b, or c is equal to 1

So far I have figured out that in order to solve this either a=1 b=1 or c=1 and either a-1=0 b-1=0 or c-1=0 and then I tried to set it up like (a-1)(b-1)(c-1)= with the entire thing equal to 0. this is how far I have gotten on that problem.

and

2. It takes three days for a boat to travel down a river (i.e. with the current) from point A to point B, and it takes four days for it to come back. How long will it take a log to float from A to B?

for this problem I know that I will be working with the formula for velocity. I also know that I will be using three different velocities, the velocity of the boat, the velocity of the river, and the velocity of the log which is essentially just the velocity of the river because a log travels by current.

Any help with these two problems would be very much appreciated!