Painters A and B take 3 hours to paint a room
Painters B and C take 5 hours to paint the same room
Painters A and C take 7 hours to paint the same room
How long would it take all three to paint the same room?
1/a + 1/b = 1/3
1/b + 1/c = 1/5
1/a + 1/c = 1/7
add them all up and you get
2/a + 2/b + 2/c = 1/3 + 1/5 + 1/7 = 71/105
1/a + 1/b + 1/c = 71/210
So, it takes 210/71 ≈ 2.95 hours for all three to do the job.
That's rather surprising, isn't it?