SOLUTION: It takes beverly 4 hours to clean a room. If steve worked together with her it would only take 48 minutes for the room to be cleaned. How long would it take steve to clean the room

Question 581296: It takes beverly 4 hours to clean a room. If steve worked together with her it would only take 48 minutes for the room to be cleaned. How long would it take steve to clean the room by himself?
I did:
1/B + 1/S= 1/X
B= beverly
S= steve
1/4hrs + 1/X= 1/48 min
Answer by ptaylor(2198) (Show Source): You can put this solution on YOUR website!
Let x=amount of time it takes Steve to clean the room working alone
Then Steve works at the rate of 1/x room per hour
Beverly works at the rate of 1/4 room per hour
Beverly and Steve working together works at the rate of 1/(4/5) =5/4 room per hour (48 min=4/5 hr and we are working in hours)
Soooo, our equation to solve is:
(1/4)+(1/x)=5/4 multiply each term by 4x
x+4=5x
4x=4
x=1 hour----amount of time it takes Steve to clean the room working alone.
CK
in 4/5 of an hour Steve cleans 4/5 th of the room
in 4/5 of an hour Beverly cleans(1/4)(4/5) =1/5 of the room
1/5+4/5=1 (room that is)
Hope this helps---ptaylor
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