SOLUTION: one person cleans the floors in 4 hours another person cleans the floors in 7 hours how long would it take if they worked together?

Question 923805: one person cleans the floors in 4 hours another person cleans the floors in 7 hours how long would it take if they worked together?
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes both persons to clean the floor working together
Then both persons, working together, cleans the floor at the rate of 1/x of the floor per hour
The first person cleans floors at the rate of 1/4 of the floor per hour
The other person cleans floors at the rate of 1/7 of the floor per hour
So, our equation to solve is:
(1/4)+(1/7)=1/x multiply each term by 28x
7x+4x=28
11x=28
x=28/11=~~~~~2.55 hours
CK----- I'll use the fractions to avoid round off errors.
In (28/11) hours, the first person cleans (28/11)*(1/4) =7/11 of the floor
In (28/11) hours, the other person cleans (28/11)*(1/7)=4/11 of the floor
(7/11)+(4/11)=1---- one cleaned floor that is
Hope this helps---ptaylor
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