SOLUTION: 90.) Solve each problem 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 rational

Algebra ->  Algebra  -> Test -> SOLUTION: 90.) Solve each problem 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 rational       Log On

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Question 164391This question is from textbook Elementary and Intermediate
: 90.) Solve each problem
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 rational expression for the fractions of the barn that they complete in one day by working together. Evaluate the expression for x = 5.This question is from textbook Elementary and Intermediate

Answer by josmiceli(9664) About Me  (Show Source):
You can put this solution on YOUR website!
Melanie's rate + Mellisa's rate = rate working together
(1 barn / x days + 1 barn / 2x days)
As an algebra expression:
1%2Fx+%2B+1%2F2x
x+=+5
1%2F5+%2B+1%2F10+=+2%2F10+%2B+1%2F10
2%2F10+%2B+1%2F10+=+3%2F10
What this says is that they can paint 3 barns in 10 days
by working together, but there is only 1 barn to paint.
I'll make a new quantity called y and I'll write
1%2Fy+=+3%2F10 This says (1 barn/y days) = (3 barns/10 days)
Solve for y by multiplying both sides by 10y
10+=+3y
y+=+10%2F3
So, working together, they can paint 1 barn in 10%2F3 days