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

Algebra ->  Rate-of-work-word-problems -> 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      Log On


   

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) About Me  (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