It takes Ralph 5 hours to paint a fence. Lisa can do the same job in 12 hours. If Ralph paints alone for 30 minutes before Lisa begins helping, how long must they work together to finish painting the fence?
My Solution:
Let x = the time it takes both to paint the fence
I do not know where 30 minutes should be in the equation.
1/5 + 1/12 = 1/x
If this is the wrong equation, why is it wrong?
How did you know where to place x?
Where did 0.9 come from?
How did you come up with the right equation?
I can now solve the problem but would love to know how you were able to design the right equation. What information in the problem led you to this equation?
Ralph’s work in 1 h = 1/5
Lisa’s work in 1 h = 1/12
Ralph and Lisa’s work in 1 h = 1/5 + 1/12 = 17/60 of whole work
Now Ralph in 1 h does 1/5 of fence
Ralph will do in 30 m = 1/10 of fence
Work left = 1-1/10 = 9/10
Ralph and Lisa can do 17/60 of work on 1 h
Ralph and Lisa can do 1 ( whole ) of work on 60/17 h
Ralph and Lisa will do 9/10 of work on 60/17 * 9/10 h = 54/17 h