SOLUTION: IT WOULD TAKE BETSEY 4 HOURS TO CLEAN HER ROOM. HER MOM COULD DO IT IN 2 HOURS. USE ALGEBRA TO FIND HOW LONG IT WOULD TAKE THEM WORKING TOGETHER?

Algebra ->  Average -> SOLUTION: IT WOULD TAKE BETSEY 4 HOURS TO CLEAN HER ROOM. HER MOM COULD DO IT IN 2 HOURS. USE ALGEBRA TO FIND HOW LONG IT WOULD TAKE THEM WORKING TOGETHER?      Log On


   

Question 387082: IT WOULD TAKE BETSEY 4 HOURS TO CLEAN HER ROOM. HER MOM COULD DO IT IN 2 HOURS. USE ALGEBRA TO FIND HOW LONG IT WOULD TAKE THEM WORKING TOGETHER?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Think of these problems as adding their
rates of working separately
Let R%5B1%5D = Betsy's rate of working alone
Let R%5B2%5D = Mother's rate of working alone
Let R%5B3%5D = their rate of working together
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The rule is:
R%5B1%5D+%2B+R%5B2%5D+=+R%5B3%5D
given:
R%5B1%5D+=+1%2F4
This means 1 room cleaned in 4 hours
R%5B2%5D+=+1%2F2
This means 1 room cleaned in 2 hours
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So far I've got
1%2F4+%2B+1%2F2+=+R%5B3%5D
I can express R%5B3%5D as 1%2Fx, or 1 room
cleaned in x hours
Now I have:
1%2F4+%2B+1%2F2+=+1%2Fx
Multiply both sides by 4x
x+%2B+2x+=+4
3x+=+4
x+=+4%2F3 hours
This is the same as:
%284%2F3%29%2A60+=+80 min, or 1 hour and 20 minutes working together