Algebra WORK Word Problem

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?

Re: Algebra WORK Word Problem

Quote:

Originally Posted by

**nycmath** 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?

right equation 1/5x+1/12x =0.9

Re: Algebra WORK Word Problem

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?

Re: Algebra WORK Word Problem

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

Re: Algebra WORK Word Problem

Quote:

Originally Posted by

**ibdutt** 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

Thank you for breaking down the solution process.

I yearn for the day when establishing an equation from application information will become second nature.