word problem: Melanie can paint a certain in x days....

[lcliff]

Barn Painting. Melanie can paint a certain barn by herself in x days. Her helper Melissa can paint the same barn by herself in 2x days. Write a rationalexpression for the fraction of the barn they can complete in one day by working together. Evluate the expression for x=5.

This is how I started but do not know if any of it is right!! Or where to go after this.

        | Rate | time | Work |
========|======|======|======|
Melanie |  1/x |   1  |  1/x |
--------|------|------|------|
Melissa | 1/2x |   1  | 1/2x |

 

[stapel]

You have "rate of work" (the amount done per unit of time) as being the same as "work". What do the two different things stand for?

Try using the standard "work" set-up:

. . . . .time to complete job (in days):
. . . . .Melanie: x
. . . . .Melissa: 2x

. . . . .completed per time unit:
. . . . .Melanie: 1/x
. . . . .Melissa: 1/(2x)

. . . . .Adding their labors: 1/x + 1/(2x)

This last is the expression they're asking. Plug in "5" for "x", and simplify.

Eliz.