I was having trouble on cracking this problem algebraically. If I draw pictures and make up numbers it makes sense. But can anyone show me how to do the problem algebraically and show it in such a way as it makes sense. Here's the problem:
Tom can paint 1 fence in 3 hours. John can paint the same fence in 2 hours. How long would it take them both to paint the same in fence if they worked together?
My first impression was this'd be really easy, and I do consider myself to be good at math. But to be honest I couldn't find a way of doing such a problem in a intuitive and understanding way.
Hopefully you guys have some fun in trying to solve this as well. ;)
Work done by Tom in $3$ hours = $1$ fence
Work done by Tom in $1$ hour = $1\over 3$ fence
Similarly, Work done by John in $1$ hour = $1\over 2$ fence
Work done in $1$ hour by the two of them = $1\over 3$ + $1\over 2$ = $5\over 6$
Time taken for $1$ fence = $1\over 5/6$ = $6\over 5$